Series & parallel circuits

A group of students investigate the circuit shown in the figure below.

There are N capacitors, each of capacitance C, connected in parallel.

There are N resistors, each of resistance R, connected in series.

Initially, the students close the switch X. They then note the reading on the ammeter.

The students then open the switch. They record the time T for the reading on the ammeter to fall to half of its initial value.

The table below shows the students’ results.

Show that T = (ln 2)N²RC. (a)

The results table is repeated below.

Complete the last column for N = 1 and N = 2 in the table below.

The students begin to plot a graph of T (y-axis) against N² (x-axis). (d)

Draw a straight line of best fit on the graph.

Calculate the gradient of the straight line of best fit.

The value of C is known to be 1000 F ± 5%.

Use your gradient value from (iii) to find a value for R, in units of k , including an absolute uncertainty.

R =........ ±........ k

Following the investigation, the students discovered that the sixth 1000 F capacitor connected to the circuit was actually two 470 F capacitors connected in parallel.

State the type of error caused by this mistake.

Explain the effect that this error would have had on the calculated value of R.

Use Fig. 19.2 to show that the p.d. across the 50 resistor is 0.50 V.

Calculate the e.m.f. E of the power supply.

The LED emits blue light of wavelength 4.7 × 10^–7 m.

Estimate the number of blue light photons emitted from the LED per second.

number of photons per second =........ s^–1

The light from the LED is incident on a metal of work function 2.3 eV.

Explain, with the help of a calculation, whether or not photoelectrons will be emitted from the surface of the metal.

A circuit is shown below.

The battery has negligible internal resistance. The temperature of the NTC thermistor is decreased.

Which of the following statements is/are correct?

1 The current at X increases. 2 The current at Y remains the same. 3 The potential difference across the thermistor increases.

A 1, 2 and 3

B Only 2 and 3

C Only 3

D Only 2

Your answer

State one S.I. base quantity other than length, mass and time.

Show that the total resistance R of the wires is given by the equation

A student uses the equation in (i) to determine R. The table below shows the data recorded by the student in her lab book.

Quantity	Value
	4.7 10−7 m
L	9.5 ± 0.1 cm
d	0.270 ± 0.003 mm

1. Name the likely instruments used by the student to measure L and d.

2. Use the data in the table and the equation in (i) to determine R and the absolute uncertainty. Write your answer to the correct number of significant figures.

3. The instrument used to measure d has a zero-error. The measured d is much larger than the actual value. Discuss how the actual value of R compares with the value calculated above.

Fig. 18.1 shows a circuit.

The cell has e.m.f. 1.5 V. The cell and the variable power supply both have negligible internal resistance.

The e.m.f. of the power supply is set at 4.2 V. Calculate the current I in the 33 resistor.

The e.m.f. of the variable supply is now slowly decreased from 4.2 V to 0 V. Describe the effect on the current I in the 33 resistor.

* A group of students are investigating the power dissipated in a variable resistor connected across the terminals of a cell. The cell has e.m.f. 1.5 V. The students determine the power P dissipated in the variable resistor of resistance R.

Fig. 18.2 shows the data points plotted by the students on a graph of P (y-axis) against R (x-axis).

The group of students know that maximum power is dissipated in the variable resistor when R is equal to the internal resistance r of the cell.

Describe, with the help of a suitable circuit diagram, how the students may have determined P and R. Use Fig. 18.2 to estimate the internal resistance r of the cell and discuss any limitations of the data plotted by the group.