Section 7: AC, circuits and internal resistance

Include the internal resistance in the total resistance, and say whether a voltage is the EMF, the lost volts or the terminal potential difference.

A lesson for this section

Section 1 style: multiple choice

Question 1Section 1 style

Which statement describes an alternating current (AC)?

Question 2Section 1 style

The p.d. of an AC supply varies between

+8.5\ \text{V}

and

-8.5\ \text{V}

. What is the rms p.d. of the supply?

Question 3Section 1 style

The graph shows how the p.d. of an AC supply varies with time. Two complete cycles take

10\ \text{ms}

and the peak p.d. is

14\ \text{V}

. What are the frequency and the rms p.d. of the supply?

Question 4Section 1 style

A resistor is connected first to a

6.0\ \text{V}

DC supply and then to an AC supply with an rms p.d. of

6.0\ \text{V}

. Which statement is correct?

Question 5Section 1 style

The rms current in a heater is

6.0\ \text{A}

. What is the peak current?

Question 6Section 1 style

A heater element of resistance

24\ \Omega

is connected to an AC supply. The peak p.d. across the element is

340\ \text{V}

. What is the average power of the heater?

Question 7Section 1 style

3.3\ \text{k}\Omega

resistor and a

6.8\ \text{k}\Omega

resistor are connected in series across a

12\ \text{V}

supply of negligible internal resistance. What is the p.d. across the

3.3\ \text{k}\Omega

resistor?

Question 8Section 1 style

In the network shown, a

2.2\ \Omega

resistor is in series with a

12\ \Omega

resistor and a

6.0\ \Omega

resistor that are connected in parallel with each other. What is the total resistance between X and Y?

Question 9Section 1 style

A lamp is rated

12\ \text{V}

24\ \text{W}

. It is connected to a

6.0\ \text{V}

supply. Assume its resistance does not change. What is the power of the lamp now?

Question 10Section 1 style

A cable of resistance

0.36\ \Omega

carries a current of

4.0\ \text{A}

. What power is wasted as heat in the cable?

Question 11Section 1 style

Resistors of

10\ \Omega

and

25\ \Omega

are connected in parallel across a supply. What is the ratio of the power in the

10\ \Omega

resistor to the power in the

25\ \Omega

resistor?

Question 12Section 1 style

12\ \text{V}

battery of negligible internal resistance is connected across two potential dividers in parallel. One divider has

2.0\ \text{k}\Omega

above

4.0\ \text{k}\Omega

; the other has

3.0\ \text{k}\Omega

above

3.0\ \text{k}\Omega

. A voltmeter of very high resistance is connected between the midpoints P and Q of the two dividers, as shown. What is the reading on the voltmeter?

Question 13Section 1 style

A thermistor and a

2.2\ \text{k}\Omega

resistor are connected in series across a

5.0\ \text{V}

supply of negligible internal resistance. A voltmeter is connected across the

2.2\ \text{k}\Omega

resistor. As the thermistor warms, its resistance falls from

4.7\ \text{k}\Omega

1.2\ \text{k}\Omega

. How does the voltmeter reading change?

Question 14Section 1 style

In the circuit shown, a

12\ \text{V}

supply of negligible internal resistance is connected to a

4.0\ \Omega

resistor

R_1

in series with two parallel branches: a

12\ \Omega

resistor

R_2

, and a switch S in series with a

6.0\ \Omega

resistor

R_3

. Switch S is closed. What is the p.d. across

R_2

Question 15Section 1 style

Two

10\ \text{k}\Omega

resistors are connected in series across a

12\ \text{V}

supply of negligible internal resistance. A voltmeter that has a resistance of

10\ \text{k}\Omega

is connected across one of the resistors. What does the voltmeter read?

Question 16Section 1 style

Which statement describes the EMF of a source?

Question 17Section 1 style

A battery of EMF

9.0\ \text{V}

and internal resistance

1.5\ \Omega

is connected to a

6.0\ \Omega

resistor. What is the terminal potential difference (t.p.d.) of the battery?

Question 18Section 1 style

A voltmeter of very high resistance is connected directly across the terminals of a cell, with nothing else connected. It reads

1.52\ \text{V}

. What does this reading give?

Question 19Section 1 style

A cell has an EMF of

1.5\ \text{V}

and an internal resistance of

0.25\ \Omega

. What is its short-circuit current?

Question 20Section 1 style

A voltmeter across a battery reads

12.0\ \text{V}

when no current flows. When a lamp is connected, the voltmeter reads

11.2\ \text{V}

and the current is

2.0\ \text{A}

. What is the internal resistance of the battery?

Question 21Section 1 style

A student measures the terminal p.d. of a battery for different currents. The straight-line graph of t.p.d. against current falls from

6.0\ \text{V}

at zero current, passes through

1.0\ \text{V}

2.0\ \text{A}

, and meets the current axis at

2.4\ \text{A}

. What are the EMF and the internal resistance of the battery?

Question 22Section 1 style

A battery with internal resistance is connected to a lamp. A second, identical lamp is then connected in parallel with the first. What happens to the t.p.d. of the battery and to the brightness of the first lamp?

Question 23Section 1 style

A battery has an EMF of

12\ \text{V}

and an internal resistance of

0.50\ \Omega

. What external resistance gives a current of

1.6\ \text{A}

Question 24Section 1 style

A cell is connected to a

2.0\ \Omega

resistor and the current is

1.2\ \text{A}

. The resistor is replaced by a

5.0\ \Omega

resistor and the current becomes

0.60\ \text{A}

. What is the EMF of the cell?

Question 25Section 1 style

Which statement describes an ideal supply?

Question 26Section 1 style

Four cells, each of EMF

1.5\ \text{V}

and internal resistance

0.20\ \Omega

, are connected in series with a

5.2\ \Omega

resistor. What is the current in the resistor?

Question 27Section 1 style

4.0\ \Omega

resistor and an

8.0\ \Omega

resistor are connected in series across a

12\ \text{V}

supply of negligible internal resistance. A lamp of resistance

8.0\ \Omega

is then connected across the

8.0\ \Omega

resistor. Assume the lamp's resistance does not change. What is the power of the lamp?

Question 28Section 1 style

A battery drives a current of

1.5\ \text{A}

through a

4.0\ \Omega

resistor. When the resistor is replaced by a

10\ \Omega

resistor, the current is

0.75\ \text{A}

. What current does the battery drive through a

5.5\ \Omega

resistor?

Question 29Section 1 style

A battery of EMF

12\ \text{V}

and internal resistance

2.0\ \Omega

is connected to a

4.7\ \Omega

resistor and a

6.8\ \Omega

resistor in series. What is the p.d. across the

6.8\ \Omega

resistor?

Section 2 style questions

An alternating supplySection 2 style · 9 marks

A signal generator gives an alternating p.d. The graph shows how this p.d. varies with time.

(a) State what is meant by an alternating current. [1]

0 words · a sentence

(b) Use the graph to state the peak p.d. of the supply, in V. [1]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(d) Calculate the frequency of the supply, in Hz. [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(e) The supply is connected across a

22\ \Omega

resistor. Calculate the average power in the resistor, in W. [3]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

Measuring the EMF of a cellSection 2 style · 8 marks

A student connects a cell in series with a variable resistor and an ammeter. A voltmeter is connected across the terminals of the cell. The student changes the resistance of the variable resistor and records the current and the terminal potential difference (t.p.d.) each time. The graph shows the results with a line of best fit.

(a) State what is meant by the EMF of a cell. [1]

0 words · a sentence

(b) Use the graph to determine the EMF of the cell, in V. [1]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(d) Calculate the short-circuit current of the cell, in A. [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(e) Explain why the terminal p.d. decreases as the current increases. [2]

0 words · a sentence or two

A temperature sensorSection 2 style · 9 marks

A thermistor and a

1.5\ \text{k}\Omega

fixed resistor are connected in series across a

6.0\ \text{V}

supply of negligible internal resistance. A voltmeter of very high resistance is connected across the fixed resistor. The resistance of the thermistor falls as its temperature rises. The table gives the resistance of the thermistor at different temperatures.

A table of the thermistor's resistance at seven temperatures: 10 degrees Celsius, 6.8 kilohms; 20, 4.5; 30, 3.0; 40, 2.2; 50, 1.8; 60, 1.5; 70, 1.2 kilohms.
Temperature / °C	Resistance / kΩ
10	6.8
20	4.5
30	3.0
40	2.2
50	1.8
60	1.5
70	1.2

(a) Calculate the voltmeter reading, in V, when the thermistor is at

20\ ^\circ\text{C}

. [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(b) At a different temperature the voltmeter reads

3.0\ \text{V}

. Use the table to find this temperature, in °C. [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

20\ ^\circ\text{C}

. [3]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(d) Explain why the voltmeter reading increases as the temperature of the thermistor rises. [2]

0 words · a sentence or two

Starting a carSection 2 style · 9 marks

A car battery has an EMF of

12.6\ \text{V}

and an internal resistance of

0.015\ \Omega

. With the engine off, the headlamps are switched on and the battery supplies a current of

9.0\ \text{A}

. The driver then operates the starter motor, which is connected in parallel with the headlamps. While the starter motor turns the engine, the current from the battery is

160\ \text{A}

(a) Calculate the t.p.d. of the battery when only the headlamps are on, in V. [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(b) Calculate the t.p.d. of the battery while the starter motor turns the engine, in V. [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

0 words · a sentence or two

(d) Calculate the power wasted inside the battery while the starter motor turns the engine, in W. [3]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).