Question

Verify that after a time of 10.0 ms, the current for the situation considered in Example 23.9 will be 0.183 A as stated.

Final Answer

Yes, the current will be $0.183\textrm{ A}$ after 10.0 ms.

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 23, Problem 72 (Problems & Exercises)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Given a circuit that initially has a current of 10.0 amps and an inductor with inductance of 7.50 millihenries, which is 7.50 times 10 to the minus 3 henries and a resistance of 3.00 ohms, we are going to verify that the current is 0.183 amps 10.0 milliseconds after the battery is removed from the circuit or a switch is switched such that the battery is disconnected. So the current will be the initial current times

*e*to the power of negative time divided by the characteristic time constant*τ*and this*τ*equals the inductance divided by the resistance so we can substitute this in here and since we are dividing by*τ*, I am going to instead multiply by its reciprocal so I am multiplying by*R*over*L*and so we have our formula for current then is*I naughte*to the negative*tR*over*L*. So that's 10.0 amps times*e*to the power of negative 10.0 times 10 to the minus 3 seconds times 3.00 ohms divided by 7.50 times 10 to the minus 3 henries and all of this is the exponent for*e*and this works out to 0.183 amps as we expected.