Question

Calculate the current flowing through an electric bulb, which consumes 2 kWh of electric energy in 5 hours, such that the resistance of the bulb is 400 Ω.

Answer 1

Given:

Energy consumed (E) = 2 kWh

Time taken (t) = 5 hours

Resistance of the bulb (R) = 400 Ω

1. Calculate the power (P) of the bulb:

Power is the rate at which electrical energy is consumed:

\[P=\frac{E}{t}\]

\[=\frac{2\text{\ kWh}}{5\text{\ hours}}\]

\[=0.4\text{\ kW}\]

Convert kilowatts (kW) into watts (W) by multiplying by 1000:

\[P=0.4\times 1000={400}\text{\ W}\]

2. Calculate the current (I):

The formula relating power, current, and resistance is:

\(P=I^{2}\times R\)

Rearranging the formula to solve for current (I):

\[I^{2}=\frac{P}{R}\]

\[I^{2}=\frac{400}{400}\]

\(I^{2}=1\)

\(I=\sqrt{1}\)

\(I={1}\text{\ A}\)