Aim for FivePhysics C: E&M

Translation between representations (TBR)

Current growing in a resistor-inductor circuit

  • Units 11 and 13
  • 12 points
  • About 28 minutes

You can use a calculator on this question, just like on exam day.

A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator and equation sheet allowed. The CED suggests 25–30 minutes.

The question

An ideal battery of emf ε, a resistor of resistance R, an inductor of inductance L (with negligible resistance), and an open switch are connected in series. The switch is closed at time t = 0.

Suggested time: 28 minutes

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Part (a)

3 points

Starting from Kirchhoff’s loop rule, derive an expression for the current I in the circuit as a function of time t after the switch is closed. Express your answer in terms of ε, R, L, and t.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

4 points

You can’t draw here, so describe the two graphs you would sketch on separate axes, from t = 0 until long after the switch is closed: (i) the current I as a function of time, and (ii) the magnitude of the potential difference VLV_L across the inductor as a function of time. Give the values at t = 0 and for large t, and show what happens at one time constant.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

1 point

Derive an expression for the energy stored in the inductor a long time after the switch is closed.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (d)

2 points

Explain how your two graphs in part (b) are consistent with each other and with Kirchhoff’s loop rule.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (e)

2 points

The inductor is replaced with one of inductance 2L (and negligible resistance), and the experiment is repeated. Compared with the original circuit, how do (i) the final, steady current and (ii) the time it takes the current to reach half of its final value change? Justify your answers.

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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