Using the Discharge Equation | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Using the Discharge Equation

The same exponential form describes charge, p.d. or current magnitude.

Match x to the question

x=x_0e^{-t/(RC)}

Symbols

Charge question

Use Q and Q₀.

p.d. question

Use V and V₀.

Current question

Use I and I₀ with the same sign convention.

The later-to-starting ratio has no unit. Put both values in the same unit before dividing.

Worked example

Current falls to 15%

A 66 μF network discharges through 54 kΩ. Find the time for current to fall to 15% (9702/42/F/M/25 Q5(c)).

\tau=RC

\tau=(54\times10^3)(66\times10^{-6})

\tau=3.6\ \mathrm{s}

0.15=e^{-t/3.6}

t=-3.6\ln(0.15)

Answer

t=6.8\ \mathrm{s}

Your turnquick check

A capacitor has time constant 3.3 s. Find the time for its p.d. to fall to 25% of the starting value.

Show worked answer

0.25=e^{-t/3.3}

t=-3.3\ln(0.25)

Answer

t=4.6\ \mathrm{s}

Common mistake

Do not assume a half-life. Use the fraction given in the question.

Using the Discharge Equation

The same exponential form describes charge, p.d. or current magnitude.

x=x_0e^{-t/(RC)}

Symbols

Charge question

Use Q and Q₀.

p.d. question

Use V and V₀.

Current question

Use I and I₀ with the same sign convention.

The later-to-starting ratio has no unit. Put both values in the same unit before dividing.

Worked example

Current falls to 15%

A 66 μF network discharges through 54 kΩ. Find the time for current to fall to 15% (9702/42/F/M/25 Q5(c)).

\tau=RC

\tau=(54\times10^3)(66\times10^{-6})

\tau=3.6\ \mathrm{s}

0.15=e^{-t/3.6}

t=-3.6\ln(0.15)

Answer

t=6.8\ \mathrm{s}

Your turnquick check

A capacitor has time constant 3.3 s. Find the time for its p.d. to fall to 25% of the starting value.

Show worked answer

0.25=e^{-t/3.3}

t=-3.3\ln(0.25)

Answer

t=4.6\ \mathrm{s}

Common mistake

Do not assume a half-life. Use the fraction given in the question.