Electric Circuits
Beginner
Ohm's Law
Source: High school physics (Chinese)
Problem
A $220$ V, $1$ kW electric stove is to be analyzed.
- What is the current when it operates normally?
- What is its resistance?
- If the effect of temperature on the resistance is neglected, what is its power when connected to a $110$ V supply?
$I \approx 4.55$ A; \quad $R = 48.4$ $\Omega$; \quad $P' = 250$ W.
(1) Normal current. From $P = UI$:
$$I = \frac{P}{U} = \frac{1000}{220} \approx 4.55 \text{ A}$$(2) Resistance. From $P = U^2/R$ (equivalent to $R = U/I$):
$$R = \frac{U^2}{P} = \frac{220^2}{1000} = 48.4 \text{ }\Omega$$(3) Power at $110$ V. With $R$ unchanged, power scales as $U^2$:
$$P' = \frac{U'^2}{R} = \frac{110^2}{48.4} = 250 \text{ W}$$Equivalently, $P' = (U'/U)^2 P = (1/2)^2 \times 1000 = 250$ W.