More DC circuits and capacitors

Coursework 16

1) Under what conditions is the potential difference across the terminals of a battery different from the emf of the battery?

Two cells with emfs and internal resistances as shown are connected to a

3.0 Ω resistor as in the diagram above.

a) Calculate the current through the 3.0 Ω resistor

b) Calculate the potential difference across each of the batteries.

(6 marks)

2) The following diagram shows a potential divider circuit consisting of an 8.0 Ω and 2.0 Ω resistor connected in series with a battery of emf 6.0 V

Calculate the potential difference between points X and Y as measured by a high resistance voltmeter

a) if the internal resistance of the battery is negligible

b) if the internal resistance of the battery is 2 Ω

What is potential difference across X and Y if the battery has negligible internal resistance but a 20.0 Ω resistor is connected in parallel with the 2.0 Ω resistor?

(6 marks)

3) In the circuit below, the light dependent resistor (LDR) is found to have a resistance of 800 Ω in moonlight and resistance 160 Ω in daylight.

a) Calculate the voltmeter reading V_m in moonlight with the switch open.

b) Calculate the value of the resistance R if the reading on the voltmeter in daylight with the switch closed is also equal to V_m.

(4 marks)

4) A car battery has an emf of 12 V. When the car is started the battery supplies a current of 105 A to the starter motor and at this time the potential difference across the battery terminals falls to 10.8 V. Find the internal resistance of the battery.

(2 marks)

5) A capacitor (C = 0.25 μF) is initially charged to a potential of 6.0 V. It is then connected across a resistor and allowed to discharge. After a time of 5.0 x 10^-3 s, the potential across the capacitor has dropped to 1.2 V. Calculate the value of the resistance.

(4 marks)

6)

In the circuit shown above the switch is initially connected to A so that the capacitor (C = 3 μF) is charged by connecting it to the battery of emf 9 V through a resistor of resistance R = 0.4 MΩ.

a) Sketch two curves on the same set of axes to show how the voltage across R and the voltage across C vary with time during the charging process.

b) What is the charge on the capacitor 2.4 s after the switch is closed?

c) What is the voltage across the resistor 3.6 s after the switch is closed?

When the capacitor is fully charged the switch is then moved to position B – so that the capacitor discharges through the resistor R.

d) Sketch two curves on the same set of axes to show how the voltage across the resistor and the voltage across the capacitor vary with time during this discharge process.

e) How long does it take for the voltage across the capacitor to fall to 2.94 V?

(10 marks)

7) A 5.0 μF capacitor is charged so that there is a potential difference of 20 kV across the plates. It is disconnected from the power source and connected across a 7.0 MΩ resistor so that it discharges. Find

a) the initial discharge current

b) the time taken for the charge on the capacitor to fall to a value of 20 mC.

c) the time taken for the capacitor voltage to fall until it is of its initial value

(6 marks)

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