Resistors and I-V characteristics

The graph shows the I – V characteristic for a semiconductor diode.

Which is true for this graph?

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 light-emitting diode (LED) emits light over a narrow range of wavelengths.

Two LEDs L_G and L_R are adjusted to give the same maximum light intensity. L_G emits green light and L_R emits red light.

Figure 3 shows how the light output of the LEDs varies with the wavelength λ.

Figure 3

Light from L_R is incident normally on a plane diffraction grating.

Determine N, the number of lines per metre on the grating.

Suggest one possible disadvantage of using the fifth-order maximum to determine N

Figure 4 shows part of the current−voltage characteristics for L_R and L_G.

When the linear part of the characteristic is extrapolated, the point at which it meets the horizontal axis gives the activation voltage V_A for the LED.

Determine, using Figure 4, V_A for L_R.

It can be shown that:

where h = the Planck constant.

Deduce a value for the Planck constant based on the data given about the LEDs.

Figure 5 shows a circuit with L_R connected to a resistor of resistance R.

The power supply has emf 6.10 V and negligible internal resistance. The current in L_R must not exceed 21.0 mA.

Deduce the minimum value of R.

An analogue voltmeter has a resistance that is much less than that of a modern digital voltmeter. Analogue meters can be damaged if the full-scale reading is exceeded. Figure 6 shows a dual-range analogue voltmeter with a zero error.

The voltmeter is set to the more sensitive range and then used in a circuit.

What is the potential difference (pd) between the terminals of the voltmeter when a full-scale reading is indicated?

Tick () one box.

Explain the use of the mirror when reading the meter.

A student corrects the zero error on the meter and then assembles the circuit shown in Figure 7. The capacitance of the capacitor C is not known.

The output pd of the power supply is set to zero. The student connects the flying lead to socket X and adjusts the output pd until the voltmeter reading is full scale (15 V). She disconnects the flying lead from socket X so that C discharges through the voltmeter.

She measures the time T ½ for the voltmeter reading V to fall from 10 V to 5 V.

She repeats this process several times.

Table 1 shows the student’s results, none of which is anomalous.

Determine the percentage uncertainty in T ½.

Show that the time constant for the discharge circuit is about 17 s.

The student thinks that the time constant of the circuit in Figure 7 is directly proportional to the range of the meter. To test her theory, she repeats the experiment with the voltmeter set to the 3 V range. She expects T ½ to be about 2.5 s.

Explain:

• what the student should do, before connecting capacitor C to the 0 V and 3 V sockets, to avoid exceeding the full-scale reading on the voltmeter

• how she should develop her procedure to get an accurate result for the time constant

• how she should use her result to check whether her theory is correct.

The student wants to find the resistance of the voltmeter when it is set to the 15 V range. She replaces C with an 820 µF capacitor and charges it to 15 V. She discharges the capacitor through the voltmeter, starting a stopwatch when V is 14 V. She records the stopwatch reading t at other values of V as the capacitor discharges.

Table 2 shows her results.

Suggest two reasons why the student selected the values of V shown in Table 2. Explain each of your answers.

Figure 8 shows a graph of the experimental data.

Show, using Figure 8, that the resistance of the voltmeter is about 16 kΩ.

Determine the current in the voltmeter at t = 10 s.

A voltmeter has a resistance of 4.0 kΩ and reads 1.0 V for every scale division on the meter.

A power supply of emf 20 V and negligible internal resistance is connected across this voltmeter and a resistor in series. The voltmeter reads two divisions.

What is the value of the resistor?

A voltmeter is used to measure potential difference for a component X.

Which row gives the position and ideal resistance for the voltmeter?