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A device has power P at voltage V. The connecting wires from the power station to the device have a finite resistance R_C. The power dissipated in the connecting wires, P_C = ______.

Asked in GSEB Board July 2021 · Heating and power in resistors

• (1) (V²R_C)/P
• (2) (PR_C)/(V²)
• (3) (P²R_C)/(V²)
• (4) (VR_C²)/P

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives (V²R_C)/P, and it is not even a power: (V²)/P is the device's own resistance, so this has units of Ω². The wires carry I = P/V, so P_C = I²R_C.
• (2) (PR_C)/(V²) forgets to square P when squaring the current: I² = (P²)/(V²), not P/(V²).
• (4) No single slip gives (VR_C²)/P; its units (V Ω² W⁻¹) are not those of power. Sanity check: P_C = I²R_C with I = P/V.

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