An incandescent electric bulb converts 20% of its power consumption into light, and the remaining power is dissipated as heat. The bulb's filament has a resistance of 200 Ω and 2 A current flows through it. If the bulb remains ON for 10 h and the rate of electricity charge is Rs. 5/unit, then which among the following is the correct amount for the money spent on producing light?

CONCEPT:

Power Consumption and Cost Calculation for an Electric Bulb

Power (P) consumed by an electrical device is given by the product of the voltage (V) across the device and the current (I) flowing through it:

P = V × I

Using Ohm's Law, where V = I × R, the power consumed can also be expressed as:

P = I² × R

Energy consumed (E) over a period of time (t) is given by:

E = P × t

Cost of electricity is typically calculated based on the energy consumed in kilowatt-hours (kWh) and the rate per unit (1 unit = 1 kWh).

EXPLANATION:

Given:

Resistance (R) = 200 Ω

Current (I) = 2 A

Time (t) = 10 h

Rate of electricity charge = Rs. 5/unit

Calculate the power consumed by the bulb:

P = I² × R

= (2 A)² × 200 Ω

= 4 × 200

= 800 W

Calculate the total energy consumed in 10 hours:

E = P × t

= 800 W × 10 h

= 8000 Wh

= 8 kWh (since 1 kWh = 1000 Wh)

Calculate the total cost of electricity:

Total cost = Energy consumed × Rate per unit

= 8 kWh × Rs. 5/kWh

= Rs. 40

Since only 20% of the power is converted into light, calculate the cost for producing light:

Cost for light = 20% of Total cost

= 0.20 × Rs. 40

= Rs. 8

Therefore, the correct amount for the money spent on producing light is Rs. 8.