Potential dividers

In Figure 2 the cell has emf ε and internal resistance r.

The current in the circuit is I.

The potential difference (pd) across R₁ is V₁ and the pd across R₂ is V₂.

Explain how the law of conservation of energy applies in this circuit. You should consider the movement of one coulomb of charge around the circuit.

Figure 3 shows a variable resistor made with a thin conducting layer on an insulating base.

The conducting layer has constant width and thickness and has connections at the ends A and B. C is a sliding contact that can move along the surface of the conducting layer between A and B.

Figure 4 shows a circuit that uses the variable resistor as a potential divider.

The variable resistor is connected to a battery of emf 3.00 V and internal resistance r The resistance of the conducting layer between A and B is 125 Ω.

The sliding contact C is moved to end B of the variable resistor. The switch is closed. The digital voltmeter reads 2.89 V.

Show that r is approximately 4.8 Ω.

C is set at of the distance between A and B. The thickness of the conducting layer is uniform so the resistance between A and C is 25.0 Ω.

Determine the voltmeter reading at this setting.

Figure 5 shows a variable resistor similar to the one shown in Figure 3 but with the following three manufacturing faults:

• at P the conducting layer changes in thickness so that AP is thinner than PB

• at Q there is a scratch into the surface of the conducting layer and across its full width

• from R to B the conducting connector is laid over the conducting layer.

The width of the conducting layer is constant.

A pd of 3.0 V is applied across A and B. C is moved from A to B.

Sketch, on the axes in Figure 6, a graph to show how the pd between A and C varies as C is moved from A to B.

Figure 4 is a plot of current – voltage data for a filament lamp L.

Figure 4

The current I was measured as the voltage V across L was increased at a steady rate. These data were obtained using a current sensor and a voltage sensor connected to a data logger. The logger recorded data at a rate of 2.5 Hz.

Determine, in V s⁻¹, the rate of increase of V.

State two advantages of using data logging for this experiment.

Figure 5 shows two circuits that can be used to collect current–voltage data.

The dc supply has an emf of 12 V and negligible internal resistance. The current sensor and the voltage sensor behave as ideal meters.

In circuit 1:

• X is used as a variable resistor with a maximum resistance of 14.9 Ω

• when X is set to maximum resistance, the resistance of L is 2.3 Ω.

In circuit 2, X is used as a potential divider.

Discuss, with reference to circuit 1 and circuit 2, whether either circuit can produce all the data shown in Figure 4. Support your answer with a calculation.

Table 2 shows some values of V that are plotted on Figure 4 and corresponding results for I and for the power P dissipated in L.

Complete Table 2.

Plot on Figure 6 a graph of P against V. You should use only the data in your completed Table 2.

L is connected to a 12 V power supply of negligible internal resistance. L then dissipates its rated power P_r.

A second lamp, identical to L, is now connected in series with L.

Determine the percentage of P_r that is dissipated in this circuit.

A student assembles the circuit in Figure 6.

The battery has an internal resistance of 2.5 Ω.

Show that the resistance of the 6.2 V, 4.5 W lamp at its working potential difference (pd) is about 9 Ω.

The terminal pd across the battery is 6.2 V.

Calculate the emf of the battery.

The student makes a variable resistor to control the brightness of the lamp.

Figure 7 shows her circuit.

She uses a resistance wire with a diameter of 0.19 mm to make the variable resistor. A 5.0 m length of this wire has a resistance of 9.0 Ω.

Calculate the resistivity of the wire.

Figure 8 shows the 5.0 m length of wire wrapped around a tube to make the variable resistor.

Two plugs connect the variable resistor into the circuit. A moveable copper contact is used to vary the length of wire in series with the lamp. When the contact is placed on the tube at one particular position, the lamp is dim. The contact is then moved slowly to the right as shown in Figure 8.

Explain, without calculation, what happens to the brightness of the lamp as the contact is moved.

The student now makes a different circuit by connecting the variable resistor in parallel with the lamp.

The contact is returned to its original position on the tube as shown in Figure 8 and the lamp is dim. The contact is again slowly moved to the right.

Explain, without calculation, what happens to the brightness of the lamp as the contact is moved.

Figure 11 shows how the resistance of an LDR varies with light intensity.

The LDR is used as part of an alarm system in a dim room. Figure 12 shows one proposal for a sensor circuit for this system.

The power supply to the sensor has an emf of 5.0 V and a negligible internal resistance. A negligible current is drawn from the sensor circuit by the alarm subsystem.

A light beam illuminates the LDR. When the light beam is broken the LDR is not illuminated by the light beam. This causes the alarm to sound.

Table 3 shows how the light intensity at the LDR changes.

Show that the current in the sensor circuit when the LDR is not illuminated by the light beam is approximately 16 µA.

The alarm sounds when the potential difference V s across the LDR changes by more than 25% of the power supply emf.

Discuss whether the circuit shown in Figure 12 is suitable. Support your answer with a calculation.

The battery in this circuit has an emf of 4.2 V and negligible internal resistance.

What are the readings on the voltmeter when the switch is open (off) and when the switch

In the circuit below, the voltmeter reading is zero.

When the temperature of the thermistor T is increased, the voltmeter reading changes.

Which change to the circuit will restore the voltmeter to zero?

In the circuit below, the initial voltmeter reading is zero.

The temperature of the negative temperature coefficient thermistor T is then increased.

Which change to the circuit could restore the voltmeter reading to zero?

Figure 7 shows a circuit designed by a student to monitor temperature changes.

The supply has negligible internal resistance and the thermistor has a resistance of 750 Ω at room temperature. The student wants the output potential difference (pd) at room temperature to be 5.0 V

The 0.25 kΩ resistor is made of 50 turns of wire that is wound around a non-conducting cylinder of diameter 8.0 mm

Determine the area of cross-section of the wire that has been used for the resistor.

The student selects a resistor rated at 0.36 W for the 0.25 kΩ resistor in Figure 7.

Determine whether this resistor is suitable.

Determine the value of R that the student should select.

Give your answer to an appropriate number of significant figures.

State and explain the effect on the output pd of increasing the temperature of the thermistor.

Which graph shows how the pd supplied V varies as the moving contact C is moved from position P to position Q?

What is the reading on a voltmeter connected between points X and Y ?