Equivalent Resistance MCQ Quiz - Objective Question with Answer for Equivalent Resistance - Download Free PDF

The correct answer is 45 Ω.

Key Points

• Two resistors of 30 Ω each connected in parallel result in an equivalent resistance of 15 Ω.
• The formula for resistors in parallel is 1Req=1R1+1R2" id="MathJax-Element-25-Frame" role="presentation" style="position: relative;" tabindex="0">1Req=1R1+1R21Req=1R1+1R2 $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ , which gives 1Req=130+130=230=115" id="MathJax-Element-26-Frame" role="presentation" style="position: relative;" tabindex="0">1Req=130+130=230=1151Req=130+130=230=115 $\frac{1}{R_{eq}} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} = \frac{1}{15}$ , hence Req=15Ω" id="MathJax-Element-27-Frame" role="presentation" style="position: relative;" tabindex="0">Req=15ΩReq=15Ω $R_{eq} = 15 \Omega$ .
• This equivalent resistance of 15 Ω is then connected in series with a 30 Ω resistor.
• The total equivalent resistance in a series connection is the sum of the individual resistances: Rtotal=Req+R3=15Ω+30Ω=45Ω" id="MathJax-Element-28-Frame" role="presentation" style="position: relative;" tabindex="0">Rtotal=Req+R3=15Ω+30Ω=45ΩRtotal=Req+R3=15Ω+30Ω=45Ω $R_{total} = R_{eq} + R_3 = 15 \Omega + 30 \Omega = 45 \Omega$ .
• Thus, the correct equivalent resistance of the entire arrangement is 45 Ω.

Additional Information

• Resistor:
  • A resistor is a passive electrical component that implements electrical resistance as a circuit element.
  • Resistors are used to reduce current flow, adjust signal levels, divide voltages, bias active elements, and terminate transmission lines, among other uses.
• Series Circuit:
  • In a series circuit, the current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component.
• Parallel Circuit:
  • In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component.
• Ohm's Law:
  • Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
  • It is usually expressed by the formula V=IR" id="MathJax-Element-29-Frame" role="presentation" style="position: relative;" tabindex="0">V=IRV=IR $V = IR$ where V is the voltage, I is the current, and R is the resistance.

The Correct answer is same.

Key Points

• Resistivity is a material property that measures how strongly a material opposes the flow of electric current.
• The resistivity of a conductor is dependent only on the material's nature and is independent of its shape and size, such as its cross-sectional area or length.
• When the cross-sectional area of a conductor is doubled, the resistance is affected (resistance decreases), but the resistivity remains unchanged.
• This is because resistivity is defined as a constant for a specific material at a given temperature, regardless of changes in its dimensions.
• The formula for resistivity is ρ = R × (A / L), where ρ represents resistivity, R is resistance, A is the cross-sectional area, and L is the length of the conductor.
• From the formula, resistivity is independent of the conductor's dimensions; it is solely determined by the intrinsic properties of the material.
• Thus, doubling the cross-sectional area affects the resistance but does not alter the inherent resistivity of the conductor.

 Additional Information

• halved
  • Halving the resistivity would imply a change in the fundamental properties of the material, which does not happen by altering the conductor's dimensions.
  • Resistivity is constant for a specific material and is independent of changes in cross-sectional area.
• one fourth
  • The term one fourth might apply to changes in resistance when the cross-sectional area is quadrupled, but it does not affect resistivity, as resistivity depends solely on the material.
• doubled
  • Doubling resistivity would require a fundamental alteration of the material properties, which is not related to changes in physical dimensions like cross-sectional area.

The correct answer is I = I1 + I2 + I3.

Key Points

• In a parallel circuit, the total current (I) flowing through the circuit is the sum of the currents flowing through each branch. Hence, I = I1 + I2 + I3.
• The voltage across each resistor in a parallel combination is the same, but the current varies depending on the resistance of each branch.
• Ohm's Law (V = IR) is used to calculate the current through each resistor when the resistance and voltage are known.
• In parallel circuits, the total current is distributed among the branches, and this is one of the key characteristics of such circuits.
• The principle of current conservation is applied here, which states that the total current entering a junction equals the total current leaving the junction.
• Parallel circuits are commonly used in electrical systems where components need to operate independently, such as in home wiring systems.

 Additional Information

• R_eq = R3 + (R2R1)/(R2 + R1)
  • This formula is incorrect for calculating the equivalent resistance in a parallel circuit. The correct formula involves the reciprocal of resistances.
  • For two resistors in parallel, the equivalent resistance is given by 1/Req = 1/R1 + 1/R2 + ....
• 1/I = 1/I1 + 1/I2 + 1/I3
  • This equation is incorrect as it misrepresents the relationship between the total current and individual branch currents in a parallel circuit.
  • The reciprocal rule applies to resistances in parallel, not currents.
• R_eq = R1 + (R2R3)/(R2 + R3)
  • This formula is also incorrect as it doesn't represent the correct calculation of equivalent resistance in a parallel circuit.
  • In a parallel circuit, the equivalent resistance is always smaller than the smallest individual resistance.

The Correct answer is less than the resistance of the individual resistors.

Key Points

• The effective resistance of a parallel combination of resistors is always less than the resistance of the smallest individual resistor in the circuit.
• In a parallel circuit, the total current through the circuit is the sum of the currents through each resistor.
• As more paths are provided for the current to flow, the overall resistance decreases.
• The formula to calculate the effective resistance for two resistors connected in parallel is:
  1/R_effective = 1/R₁ + 1/R₂.
• This relationship ensures that the effective resistance is always less than any of the individual resistances.
• For example, if two resistors with resistances of 10 Ω and 20 Ω are connected in parallel, the effective resistance will be around 6.67 Ω, which is less than both 10 Ω and 20 Ω.
• Parallel resistors are commonly used in circuits to reduce resistance and allow more current to flow.

The correct answer is All in series.

Key Points

• When resistances are connected in series, the total resistance is the sum of individual resistances.
• The formula for total resistance in series is: \(R_{total}=R_1+R_2+R_3\).
• For resistances of 3Ω, 4Ω, and 6Ω in series, the total resistance is 3 + 4 + 6 = 13Ω.
• In a series circuit, the current flowing through each resistor is the same.
• Resistors in series provide a higher total resistance than any individual resistor.

Additional Information

• Parallel Circuit:
  • In a parallel circuit, the total resistance is less than the smallest resistor in the circuit.
  • The formula for total resistance in parallel is \(\frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\).
  • Parallel circuits are used to reduce the overall resistance and to provide the same voltage across all components.
• Ohm's Law:
  • Ohm's Law states that \(V=IR\), where V is voltage, I is current, and R is resistance.
  • This law is fundamental in understanding the behavior of electrical circuits.
• Applications of Resistors:
  • Resistors are used to control current flow in circuits.
  • They are essential in setting voltage levels and for timing applications in electronic devices.

The correct answer is 45 Ω.

Key Points

• Two resistors of 30 Ω each connected in parallel result in an equivalent resistance of 15 Ω.
• The formula for resistors in parallel is 1Req=1R1+1R2" id="MathJax-Element-25-Frame" role="presentation" style="position: relative;" tabindex="0">1Req=1R1+1R21Req=1R1+1R2 $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ , which gives 1Req=130+130=230=115" id="MathJax-Element-26-Frame" role="presentation" style="position: relative;" tabindex="0">1Req=130+130=230=1151Req=130+130=230=115 $\frac{1}{R_{eq}} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} = \frac{1}{15}$ , hence Req=15Ω" id="MathJax-Element-27-Frame" role="presentation" style="position: relative;" tabindex="0">Req=15ΩReq=15Ω $R_{eq} = 15 \Omega$ .
• This equivalent resistance of 15 Ω is then connected in series with a 30 Ω resistor.
• The total equivalent resistance in a series connection is the sum of the individual resistances: Rtotal=Req+R3=15Ω+30Ω=45Ω" id="MathJax-Element-28-Frame" role="presentation" style="position: relative;" tabindex="0">Rtotal=Req+R3=15Ω+30Ω=45ΩRtotal=Req+R3=15Ω+30Ω=45Ω $R_{total} = R_{eq} + R_3 = 15 \Omega + 30 \Omega = 45 \Omega$ .
• Thus, the correct equivalent resistance of the entire arrangement is 45 Ω.

Additional Information

• Resistor:
  • A resistor is a passive electrical component that implements electrical resistance as a circuit element.
  • Resistors are used to reduce current flow, adjust signal levels, divide voltages, bias active elements, and terminate transmission lines, among other uses.
• Series Circuit:
  • In a series circuit, the current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component.
• Parallel Circuit:
  • In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component.
• Ohm's Law:
  • Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
  • It is usually expressed by the formula V=IR" id="MathJax-Element-29-Frame" role="presentation" style="position: relative;" tabindex="0">V=IRV=IR $V = IR$ where V is the voltage, I is the current, and R is the resistance.

The Correct answer is same.

Key Points

• Resistivity is a material property that measures how strongly a material opposes the flow of electric current.
• The resistivity of a conductor is dependent only on the material's nature and is independent of its shape and size, such as its cross-sectional area or length.
• When the cross-sectional area of a conductor is doubled, the resistance is affected (resistance decreases), but the resistivity remains unchanged.
• This is because resistivity is defined as a constant for a specific material at a given temperature, regardless of changes in its dimensions.
• The formula for resistivity is ρ = R × (A / L), where ρ represents resistivity, R is resistance, A is the cross-sectional area, and L is the length of the conductor.
• From the formula, resistivity is independent of the conductor's dimensions; it is solely determined by the intrinsic properties of the material.
• Thus, doubling the cross-sectional area affects the resistance but does not alter the inherent resistivity of the conductor.

 Additional Information

• halved
  • Halving the resistivity would imply a change in the fundamental properties of the material, which does not happen by altering the conductor's dimensions.
  • Resistivity is constant for a specific material and is independent of changes in cross-sectional area.
• one fourth
  • The term one fourth might apply to changes in resistance when the cross-sectional area is quadrupled, but it does not affect resistivity, as resistivity depends solely on the material.
• doubled
  • Doubling resistivity would require a fundamental alteration of the material properties, which is not related to changes in physical dimensions like cross-sectional area.

The correct answer is I = I1 + I2 + I3.

Key Points

• In a parallel circuit, the total current (I) flowing through the circuit is the sum of the currents flowing through each branch. Hence, I = I1 + I2 + I3.
• The voltage across each resistor in a parallel combination is the same, but the current varies depending on the resistance of each branch.
• Ohm's Law (V = IR) is used to calculate the current through each resistor when the resistance and voltage are known.
• In parallel circuits, the total current is distributed among the branches, and this is one of the key characteristics of such circuits.
• The principle of current conservation is applied here, which states that the total current entering a junction equals the total current leaving the junction.
• Parallel circuits are commonly used in electrical systems where components need to operate independently, such as in home wiring systems.

 Additional Information

• R_eq = R3 + (R2R1)/(R2 + R1)
  • This formula is incorrect for calculating the equivalent resistance in a parallel circuit. The correct formula involves the reciprocal of resistances.
  • For two resistors in parallel, the equivalent resistance is given by 1/Req = 1/R1 + 1/R2 + ....
• 1/I = 1/I1 + 1/I2 + 1/I3
  • This equation is incorrect as it misrepresents the relationship between the total current and individual branch currents in a parallel circuit.
  • The reciprocal rule applies to resistances in parallel, not currents.
• R_eq = R1 + (R2R3)/(R2 + R3)
  • This formula is also incorrect as it doesn't represent the correct calculation of equivalent resistance in a parallel circuit.
  • In a parallel circuit, the equivalent resistance is always smaller than the smallest individual resistance.

The Correct answer is less than the resistance of the individual resistors.

Key Points

• The effective resistance of a parallel combination of resistors is always less than the resistance of the smallest individual resistor in the circuit.
• In a parallel circuit, the total current through the circuit is the sum of the currents through each resistor.
• As more paths are provided for the current to flow, the overall resistance decreases.
• The formula to calculate the effective resistance for two resistors connected in parallel is:
  1/R_effective = 1/R₁ + 1/R₂.
• This relationship ensures that the effective resistance is always less than any of the individual resistances.
• For example, if two resistors with resistances of 10 Ω and 20 Ω are connected in parallel, the effective resistance will be around 6.67 Ω, which is less than both 10 Ω and 20 Ω.
• Parallel resistors are commonly used in circuits to reduce resistance and allow more current to flow.

The correct answer is (R_2)/(R_1).

Key Points

• When two resistances, R1 and R2, are connected in parallel, the voltage across each resistor is the same.
• The power dissipated in a resistor in a parallel circuit is given by P = V^2 / R, where V is the voltage across the resistor and R is the resistance.
• The ratio of power dissipation in two resistors connected in parallel can be found using the formula P1/P2 = R2/R1.
• Thus, the ratio of power loss in the two resistors R1 and R2 is (R_2)/(R_1).
• This ratio indicates that the resistor with lower resistance will dissipate more power compared to the resistor with higher resistance when connected in parallel.

Additional Information

• Ohm's Law: Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points. It is mathematically expressed as V = IR.
• Power Dissipation: Power dissipation in a resistor is the rate at which energy is converted from electrical energy to heat and is given by P = I^2 * R or P = V^2 / R.
• Parallel Circuits: In a parallel circuit, components are connected across common points or junctions, leading to multiple paths for current flow. The voltage across each component in parallel is the same.
• Equivalent Resistance in Parallel: The reciprocal of the equivalent resistance of resistors connected in parallel is the sum of the reciprocals of their individual resistances: 1/Req = 1/R1 + 1/R2 + ... + 1/Rn.
• Kirchhoff's Current Law (KCL): KCL states that the total current entering a junction is equal to the total current leaving the junction. This is crucial in analyzing parallel circuits.

The correct answer is 45 Ω.

Key Points

• Two resistors of 30 Ω each connected in parallel result in an equivalent resistance of 15 Ω.
• The formula for resistors in parallel is 1Req=1R1+1R2" id="MathJax-Element-25-Frame" role="presentation" style="position: relative;" tabindex="0">1Req=1R1+1R21Req=1R1+1R2 $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ , which gives 1Req=130+130=230=115" id="MathJax-Element-26-Frame" role="presentation" style="position: relative;" tabindex="0">1Req=130+130=230=1151Req=130+130=230=115 $\frac{1}{R_{eq}} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} = \frac{1}{15}$ , hence Req=15Ω" id="MathJax-Element-27-Frame" role="presentation" style="position: relative;" tabindex="0">Req=15ΩReq=15Ω $R_{eq} = 15 \Omega$ .
• This equivalent resistance of 15 Ω is then connected in series with a 30 Ω resistor.
• The total equivalent resistance in a series connection is the sum of the individual resistances: Rtotal=Req+R3=15Ω+30Ω=45Ω" id="MathJax-Element-28-Frame" role="presentation" style="position: relative;" tabindex="0">Rtotal=Req+R3=15Ω+30Ω=45ΩRtotal=Req+R3=15Ω+30Ω=45Ω $R_{total} = R_{eq} + R_3 = 15 \Omega + 30 \Omega = 45 \Omega$ .
• Thus, the correct equivalent resistance of the entire arrangement is 45 Ω.

Additional Information

• Resistor:
  • A resistor is a passive electrical component that implements electrical resistance as a circuit element.
  • Resistors are used to reduce current flow, adjust signal levels, divide voltages, bias active elements, and terminate transmission lines, among other uses.
• Series Circuit:
  • In a series circuit, the current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component.
• Parallel Circuit:
  • In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component.
• Ohm's Law:
  • Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
  • It is usually expressed by the formula V=IR" id="MathJax-Element-29-Frame" role="presentation" style="position: relative;" tabindex="0">V=IRV=IR $V = IR$ where V is the voltage, I is the current, and R is the resistance.

The correct answer is All in series.

Key Points

• When resistances are connected in series, the total resistance is the sum of individual resistances.
• The formula for total resistance in series is: \(R_{total}=R_1+R_2+R_3\).
• For resistances of 3Ω, 4Ω, and 6Ω in series, the total resistance is 3 + 4 + 6 = 13Ω.
• In a series circuit, the current flowing through each resistor is the same.
• Resistors in series provide a higher total resistance than any individual resistor.

Additional Information

• Parallel Circuit:
  • In a parallel circuit, the total resistance is less than the smallest resistor in the circuit.
  • The formula for total resistance in parallel is \(\frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\).
  • Parallel circuits are used to reduce the overall resistance and to provide the same voltage across all components.
• Ohm's Law:
  • Ohm's Law states that \(V=IR\), where V is voltage, I is current, and R is resistance.
  • This law is fundamental in understanding the behavior of electrical circuits.
• Applications of Resistors:
  • Resistors are used to control current flow in circuits.
  • They are essential in setting voltage levels and for timing applications in electronic devices.

The correct answer is Total resistance is equal to the sum of all individual resistances..

Key Points

• In a series circuit, the total resistance (R_total) is the sum of all individual resistances (R₁, R₂, R₃, etc.).
• The formula to calculate total resistance in a series circuit is: R_total = R₁ + R₂ + R₃ + ...
• This means that the more resistors you add to the series circuit, the higher the total resistance becomes.
• Unlike parallel circuits, in a series circuit, the current has only one path to travel, thus the total resistance is simply the additive sum of all resistances.

Additional Information

• Ohm's Law:
  • Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R).
  • The formula is V = I * R.
• Series Circuit Characteristics:
  • In a series circuit, the same current flows through all components.
  • If one component fails, the entire circuit is interrupted.
• Parallel Circuit:
  • In a parallel circuit, the voltage across each component is the same.
  • The total resistance is less than the smallest individual resistance.
  • The formula for total resistance in a parallel circuit is 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
• Applications of Series Circuits:
  • Series circuits are commonly used in applications where the operation of the circuit depends on each component functioning correctly, such as in string lights.
  • They are also used in voltage divider circuits.

The Correct answer is 0.25 A.

Key Points

• When resistors are connected in series, their resistances add up. The total resistance in the circuit is calculated as:
  Total Resistance, R = R₁ + R₂ + R₃, where R₁ = 15 Ω, R₂ = 35 Ω, R₃ = 50 Ω.
• Substituting the values, R = 15 Ω + 35 Ω + 50 Ω = 100 Ω.
• The current flowing in the circuit can be calculated using Ohm's Law, which states:
  I = V / R, where I is the current, V is the voltage, and R is the total resistance.
• Given that the voltage of the battery is 25 V, we substitute the values to find the current:
  I = 25 V / 100 Ω = 0.25 A.
• Thus, the current flowing in the circuit is 0.25 A, which is the correct answer.
• This calculation is significant in understanding the behavior of resistors in series circuits and applying Ohm's Law effectively.

 Additional Information

• Ohm's Law
  • Ohm's Law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant.
  • Mathematically, it is expressed as V = IR, where V is the voltage, I is the current, and R is the resistance.
  • It is one of the fundamental principles used in electrical and electronic circuits.
• Series Circuits
  • In a series circuit, the same current flows through all the components connected in the series.
  • The total resistance is the sum of individual resistances, which increases as more resistors are added.
  • Such circuits are used in applications where equal current flow through all components is required, like in string lights.

The Correct answer is same.

Key Points

• Resistivity is a material property that measures how strongly a material opposes the flow of electric current.
• The resistivity of a conductor is dependent only on the material's nature and is independent of its shape and size, such as its cross-sectional area or length.
• When the cross-sectional area of a conductor is doubled, the resistance is affected (resistance decreases), but the resistivity remains unchanged.
• This is because resistivity is defined as a constant for a specific material at a given temperature, regardless of changes in its dimensions.
• The formula for resistivity is ρ = R × (A / L), where ρ represents resistivity, R is resistance, A is the cross-sectional area, and L is the length of the conductor.
• From the formula, resistivity is independent of the conductor's dimensions; it is solely determined by the intrinsic properties of the material.
• Thus, doubling the cross-sectional area affects the resistance but does not alter the inherent resistivity of the conductor.

 Additional Information

• halved
  • Halving the resistivity would imply a change in the fundamental properties of the material, which does not happen by altering the conductor's dimensions.
  • Resistivity is constant for a specific material and is independent of changes in cross-sectional area.
• one fourth
  • The term one fourth might apply to changes in resistance when the cross-sectional area is quadrupled, but it does not affect resistivity, as resistivity depends solely on the material.
• doubled
  • Doubling resistivity would require a fundamental alteration of the material properties, which is not related to changes in physical dimensions like cross-sectional area.