Question

An electric heater is rated at 300W for use in a 110V circuit. the circuit breaker in the circuit can handle 12A of current. 4 heater can be safely operated in the circuit because...

Answer 1

An electric heater is rated at 300W for use in a 110V circuit. The circuit breaker in the circuit can handle 12A of current. 4 heaters can be safely operated in the circuit because...

**Solution.**

$$P = 300W, V = 110V, I_b = 12A;$$ $$I - ?$$

$I_b$ – the peak current which circuit breaker in the circuit can handle.

The resistance of the heater by the formula of the electric power of the heater:

$$P = \frac{V^2}{R}.$$ $$R = \frac{V^2}{P}.$$

4 heaters operate in the 110V circuit in parallel as on the diagram.

The resistance $R^*$ of 4 heaters:

$$\frac{1}{R^*} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R};$$ $$R ^ {*} = \frac {R}{4};$$ $$R = \frac {V ^ {2}}{P};$$ $$R ^ {*} = \frac {V ^ {2}}{4 P}.$$

By Ohm's law the current in the circuit with 4 heaters:

$$I = \frac {V}{R ^ {*}};$$ $$R ^ {*} = \frac {V ^ {2}}{4 P};$$ $$I = \frac {V 4 P}{V ^ {2}};$$ $$I = \frac {4 P}{V}.$$ $$I = \frac {4 \cdot 300}{110} = 10.9 (A).$$

The current in the circuit with 4 heaters is $I = 10.9A$.

The circuit breaker in the circuit can handle $I_{b} = 12A$ of current and less current..

$$10.9 A < 12 A;$$ $$I < I _ {b}.$$

The circuit breaker in the circuit can handle of the current in the circuit with 4 heaters.

**Answer:** 4 heaters can be safely operated in the circuit because the current in the circuit is less than the peak current which circuit breaker in the circuit can handle.