Many domestic appliances are designed to operate at a fixed rated voltage. In practice the mains voltage can fluctuate slightly around its nominal value. Let the fractional change in the supply voltage be VΔV, where ΔV may be positive or negative. The resistance of the appliance is assumed to stay constant over this range.
(i) Starting from the relation P=RV2, derive an expression showing that the fractional change in power PΔP is related to the fractional change in voltage by PΔP=2VΔV+(VΔV)2. Clearly state the algebraic steps involved.
(ii) For a voltage drop of 8% (i.e.
VΔV=−0.08), calculate the approximate percentage change in power, retaining terms up to (VΔV)2. State whether the power increases or decreases.
(iii) Briefly comment on why even small variations in mains voltage can lead to appreciable changes in the power consumption of purely resistive devices.