charge variation

Electricity and Magnetism Level 2

a battery of 10 V is connected to a resistance of 20 ohm through a variable resistance R the amount of charge which has passed in the circuit in 4 minutes if the variable resistance R is increased at the rate of 5 ohm/min

60ln2 C 120C 120ln2 C 240ln2 C

1 solution

Caleb Townsend
Feb 17, 2015

We know that $I = \frac{dQ}{dt}$ and $I = \frac{V}{R}.$ Set the two equal to one another and solve for $dQ$ then integrate. $dQ = \frac{V}{R}dt$ $Q = \int\frac{V}{R}dt$ Convert minutes to seconds (base unit) and integrate to get $Q = \int_0^{240} \frac{10 V}{(20 + t/12)\Omega}dt = 120 \ln 2\ C$

charge variation

1 solution

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