Two resistors, each of 30 Ω are connected in parallel. The combination is connected in series to a third resistor of 30 N. The equivalent resistance of this arrangement is:

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 $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ , which gives $\frac{1}{R_{eq}} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} = \frac{1}{15}$ , hence $R_{eq} = 15 \Omega$ .
• 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: $R_{total} = R_{eq} + R_3 = 15 \Omega + 30 \Omega = 45 \Omega$ .
• 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 $V = IR$ where V is the voltage, I is the current, and R is the resistance.