First slide

Electrical power

Question

In a circuit shown in fig. the heat produced in 5 ohm resistor due to a current flowing in it is 10 calories per second. The heat produced in 4 ohm resistor is

Difficult

A

1 cal per sec
B

2 cal per sec
C

3 cal per sec
D

4 cal per sec

Solution

Resistance of upper branch, R₁ $= 10 Ω$
Resistance of lower branch, R₂ = 5 $Ω$
As they are connected in parallel, hence potential difference across each will be same = V
Given that $\frac{V^{2}}{4 \cdot 2 R_{2}} = 10 cal / \sec$
$∴ V^{2} = 4 \cdot 2 \times 10 \times 5 = 210$
or $V = \sqrt{(210)} volt$
Current in 4 $Ω$ resistance
$= (V / R_{1}) = {\sqrt{(210)} / 10}$
Heat produced $= (i^{2} R / 4 \cdot 2) cal / \sec$
$= \frac{210}{100} \times \frac{4}{4 \cdot 2} = 2 cal / \sec$

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