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प्रश्न
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.
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उत्तर
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):
\[I^{2}=\frac{P}{R}\]
\[I^{2}=\frac{400}{400}\]
\(I^{2}=1\)
\(I=\sqrt{1}\)
\(I={1}\text{\ A}\)
