A dc circuit shown below has a voltage V, a current source

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A dc circuit shown below has a voltage V, a current source I and several resistors. A particular resistor R dissipates a power of 4W when V alone is active. The same resistor dissipates a power of 9W when I alone is active. The power dissipated by R when both sources are active will be—

1. 1W
2. 5W
3. 13W
4. 25W

Correct Option: D

The given circuit:

Resistive network Applying superposition theorem (since here one energy source is acting at a time)
● When only voltage source is active:
V²/R = 4W = I²R
Let R = 1Ω
Assume I₁ = I = 4 = 2A
● When only current source is active
I²R = 9W
or
I² = 9W
Assume
I₂2 = I² = 9
or
I₂ = 3A
Since current flowing in both the case follow the same direction. Therefore, net current will add up.
So,
I = I₁ + I₂ = 2 + 3 = 5A
Now, the power dissipated by R when both sources are active will be:
P=I₂R = 52.1 = 25W
Hence alternative (D) is the correct choice.