Smoothing Calculations | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Smoothing Calculations

Between recharge peaks, treat the smoothing capacitor like the discharging capacitor from the Capacitance chapter.

Use two points on one discharge

V=V_0e^{-t/RC}

Symbols

Choose two voltage readings from the same falling part of one ripple. Do not cross a recharge peak.
Measure the time interval and convert it to seconds.
Use the voltage ratio to find the required quantity.

Worked example

Find the load resistance

A 570 μF capacitor falls from 12 V to 8.0 V in 7.3 ms. Find the load resistance.

8.0=12e^{-7.3\times10^{-3}/RC}

RC=\dfrac{-7.3\times10^{-3}}{\ln(8.0/12)}

RC=1.8\times10^{-2}\ \mathrm{s}

R=\dfrac{1.8\times10^{-2}}{570\times10^{-6}}

Answer

R=32\ \Omega

This is the 2025 mark-scheme method and result (9702/41/M/J/25 Q6(b)(iv)–(c)).

Common mistake

The two voltages must lie on one discharge. A recharge peak resets the starting voltage and breaks that exponential interval.

Your turnnumerical check

A 470 μF capacitor falls from 10 V to 7.0 V in 5.0 ms between recharge peaks. Calculate the load resistance.

Show worked answer

7.0=10e^{-5.0\times10^{-3}/RC}

R=\dfrac{-5.0\times10^{-3}}{470\times10^{-6}\ln(7.0/10)}

Answer

R=30\ \Omega

Smoothing Calculations

Between recharge peaks, treat the smoothing capacitor like the discharging capacitor from the Capacitance chapter.

V=V_0e^{-t/RC}

Symbols

Choose two voltage readings from the same falling part of one ripple. Do not cross a recharge peak.
Measure the time interval and convert it to seconds.
Use the voltage ratio to find the required quantity.

Worked example

Find the load resistance

A 570 μF capacitor falls from 12 V to 8.0 V in 7.3 ms. Find the load resistance.

8.0=12e^{-7.3\times10^{-3}/RC}

RC=\dfrac{-7.3\times10^{-3}}{\ln(8.0/12)}

RC=1.8\times10^{-2}\ \mathrm{s}

R=\dfrac{1.8\times10^{-2}}{570\times10^{-6}}

Answer

R=32\ \Omega

This is the 2025 mark-scheme method and result (9702/41/M/J/25 Q6(b)(iv)–(c)).

Common mistake

The two voltages must lie on one discharge. A recharge peak resets the starting voltage and breaks that exponential interval.

Your turnnumerical check

A 470 μF capacitor falls from 10 V to 7.0 V in 5.0 ms between recharge peaks. Calculate the load resistance.

Show worked answer

7.0=10e^{-5.0\times10^{-3}/RC}

R=\dfrac{-5.0\times10^{-3}}{470\times10^{-6}\ln(7.0/10)}

Answer

R=30\ \Omega