A charge of $6$ $6$ $C$ $C$ passes through a circuit every $3$ $3$ $s$ $s$ . If the circuit can generate $24$ $24$ $W$ $W$ of power, what is the circuit's resistance?

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A charge of $6$ $6$ $C$ $C$ passes through a circuit every $3$ $3$ $s$ $s$ . If the circuit can generate $24$ $24$ $W$ $W$ of power, what is the circuit's resistance?

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Answer 1 · 2016-08-06T23:02:35

Current is given by $I = \frac{Q}{t}$ $I=Q/t$ , so in this case is $I = \frac{6}{3} = 2$ $I=6/3=2$ $A$ $A$ .

Power in an electric circuit is given by $P = I^{2} R$ $P=I^2R$ , which we can rearranged to make $R$ $R$ the subject: $R = \frac{P}{I^{2}} = \frac{24}{2^{2}} = 6$ $R=P/I^2=24/2^2=6$ $Omega$ .

Explanation:

Very briefly as an additional explanation, we often just remember Ohm's Law, $V=IR$ , and $P=VI$ for power, and substitute to find the expression we need. In this case, substituting in $IR$ for $V$ in the law for power gives us $P=IRxxI=I^2R$ .

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A charge of $6$ $6$ $C$ $C$ passes through a circuit every $3$ $3$ $s$ $s$ . If the circuit can generate $24$ $24$ $W$ $W$ of power, what is the circuit's resistance?

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A charge of $6$ $6$ $C$ $C$ passes through a circuit every $3$ $3$ $s$ $s$ . If the circuit can generate $24$ $24$ $W$ $W$ of power, what is the circuit's resistance?