AP Physics C E and M 11.5: Internal Resistance

Describe a circuit with resistive wires and a battery with internal resistance, relating emf, terminal potential difference, and current.

[Maximum number: 3]

Students are asked to determine the resistance R of identical resistors $\mathrm{R}_{\mathrm{A}}$ and $\mathrm{R}_{\mathrm{B}}$ . The resistors are connected in series with each other, a battery of known emf $\mathcal{E}$ , an inductor of known inductance L, and a switch, as shown in Figure 1. The students have access to a voltmeter that can measure potential difference as a function of time. The students are required to measure a quantity that increases with time to determine R.

Indicate whether $\left|\Delta V_{2}\right|$ is greater than, less than, or equal to $\left|\Delta V_{1}\right|$ .

\left|\Delta V_{2}\right|>\left|\Delta V_{1}\right| \quad-\left|\Delta V_{2}\right|<\left|\Delta V_{1}\right| \quad-\left|\Delta V_{2}\right|=\left|\Delta V_{1}\right|

Justify your answer.

Figure 1

For selecting $\left|\Delta V_{2}\right|<\left|\Delta V_{1}\right|$ with an attempt at a relevant justification For indicating that the total resistance has increased For indicating that the current decreases due to the increased resistance 1 point

OR

For indicating that the potential difference across the inductor will increase, and, therefore, the potential difference across $\mathrm{R}_{\mathrm{A}}$ must decrease

Example Response
$\left|\Delta V_{2}\right|<\left|\Delta V_{1}\right|$ , because the inductor has nonnegligible resistance, and the total resistance of the new circuit increases as compared to the original circuit. Therefore, the current in the new circuit is reduced compared to that of the original circuit when steady-state conditions are established.

OR
$\left|\Delta V_{2}\right|<\left|\Delta V_{1}\right|$ , because the inductor has nonnegligible resistance, and the total resistance of the new circuit increases as compared to the original circuit. Therefore, the potential difference across the inductor increases, which decreases the potential difference across $\mathrm{R}_{\mathrm{A}}$ compared to that of the original circuit when steady-state conditions are established.

Total for part (d)

for question 2

15 points

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11.5.B—Describe a circuit with resistive wires and a battery with internal resistance question 1