First slide

Electrical power

Question

For ensuring dissipation of same energy in all three resistors (R₁, R₂ and R₃) connected as shown in figure, their values must be related as:

Moderate

A

R₁ = R₂ = R₃
B

R₂ = R₃ and R₁ = 4R₂
C

R₂ = R₃ and R₂ = 4R₁
D

R₁ = R₂ + R₃

Solution

If R₂ = R₃ and R₂ = 4R₁, then
Now, $P_{R_{1}} = \frac{{(V / 3)}^{2}}{R_{1}} = \frac{V^{2}}{9 R_{1}}$
$P_{R_{2}} = \frac{{(2 V / 3)}^{2}}{4 R_{1}} = \frac{V^{2}}{9 R_{1}} and P_{R_{3}} = \frac{{(2 V / 3)}^{2}}{4 R_{1}} = \frac{V^{2}}{9 R_{1}}$

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