Question

The electric power delivered by a transmission cable of resistance \( R_c \) at a voltage \( V \) is \( P \). The power dissipated is

• A. \( \frac{PV}{R_c} \)
• B. \( \frac{PR_c}{V} \)
• C. \( PVR_c \)
• D. \( \frac{P^2 R_c}{V^2} \)
• E. \( \frac{P^2 R_c^2}{V} \)

Hint:

For resistive circuits, the power dissipated is proportional to the square of the voltage divided by the resistance.

Answer 1

The Correct Option is D

The power dissipated by a transmission cable is related to the voltage across the cable and its resistance by the formula: \[ P = \frac{V^2}{R_c} \] This implies that the power dissipated by the resistance \( R_c \) is proportional to the square of the voltage and inversely proportional to the resistance. Thus, the power dissipated is: \[ {Power dissipated} = \frac{P^2 R_c}{V^2} \] Hence, the correct answer is (D).