A charge of $25 C$ passes through a circuit every $4 s$ . If the circuit can generate $25 W$ of power, what is the circuit's resistance?

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Answer 1 · 2018-06-26T09:58:23

$0.64$ ohms.

We first find the current passing through, which is given by the equation:

$I=Q/t$

where:

$I$ is the current in amperes

$Q$ is the charge in coulombs

$t$ is the time in seconds

So, the current is:

$I=(25 \ "C")/(4 \ "s")$

$=6.25 \ "A"$

Power is related through current and resistance by the equation:

$P=I^2R$

where:

$P$ is the power in watts

$I$ is the current in amperes

$R$ is the resistance in ohms

Rearranging for resistance, we get:

$R=P/I^2$

Plugging in the values, we get:

$R=(25 \ "W")/((6.25 \ "A")^2)$

$=(25 \ "W")/(39.0625 \ "A"^2)$

$=0.64 \ Omega$

A charge of 25 C25 C passes through a circuit every 4 s4 s. If the circuit can generate 25 W25 W of power, what is the circuit's resistance?