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Edexcel | Physics WPH0 | S 11 6 1 | 1 hour 30 minutes
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  • Q1
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  • Q4
4
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A designer needs a circuit that will cause a delay in switching off the interior light in a

car after the door is shut.

She uses a circuit with a resistor and a capacitor. She knows that the time constant T is

given by

                                                  T = RC

where R is the resistance in ohms and C is the capacitance in farads.

With the switch in position X the capacitor is charged to 12 V. When the switch is

moved to position Y the capacitor discharges through the resistor and the potential

difference (p.d.) across the resistor falls steadily from 12 V.

4
(a) (I)
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1 Mark

Calculate a theoretical value for the time constant for this circuit.

Time constant =

Answer = 22 s

Example of calculation

4
(a) (II)
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1 Mark

What is the significance of the time constant for such a discharge?

Time taken for the p.d/charge/current to change by 63%

or to fall to 1/e of its original value or to fall to (12/e)V or to fall

to 4.41 V

4
(b)
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She decides to check the theoretical value for the time constant T using a stopwatch,

with a precision of 0.01s.

4
(b) (I)
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1 Mark

State why the voltmeter needs to have a high resistance.

 

To reduce/prevent charge/current through the voltmeter.

4
(b) (II)
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1 Mark

State why a stopwatch is suitable for measuring the time in this context.

Precision of stopwatch much less than reaction time

or

uncertainty significantly less than 22 s.

4
(b) (III)
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1 Mark

State what she should do to make her value for T as reliable as possible.

Repeat experiment and calculate mean value

or

use graphical method

4
(c)
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2 Mark s

For a capacitor discharging through a resistor, the potential difference V across the

resistor at time t is given by

                                             

Explain why a graph of ln V against t should be a straight line.

Correct expansion ln V = - t/RC + ln V0

Compare with                y = mx + c

or

state that RC is constant

4
(d)
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4 Mark s

The designer uses the circuit to obtain the following data.

Plot a graph on the grid opposite to show that these data are consistent with

Use the extra column in the table above for your processed data.

ln values correct and to at least 2DP

Labels axes with quantity and unit; y-axis must be labelled ln (V/V)

Scales, (expect 1cm:0.1 vertically)

Points correctly plotted and best straight line

4
(e) (I)
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2 Mark s

Use your graph to obtain another value for the time constant.

Time constant from the graph =

Large triangle (at least half the drawn line) with correct values

Correct calculation for T in range 19.8 < T < 20.2 and at least 3 SF

(no unit penalty)

4
(e) (II)
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1 Mark

Calculate the percentage difference between your value from the graph and the

theoretical value from (a)(i).

Percentage difference =

Uses 22 s and graph value to calculate % difference correctly

Example of calculation

(20.0 – 22.0)/22 = 2.0/22 = 9.1%

4
(f) (I)
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2 Mark s

Use your graph to find how long it takes for the p.d. to decrease to 5.0 V.

Add to your graph to show how you did this.

ln 5 (=1.609) used to find time from graph

Value in range 17.4 s – 17.6 s and to 3 SF

4
(f) (II)
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1 Mark

The designer wants the p.d. to decrease to 5 V in about 12 s.

Mark with a cross ( ) the value of R she should use.

Answer = 150 kΩ (option C)

Example of calculation

220 x (12/17.5) = 150

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