ConceptConceptDocsDocuments

CAIE A-Level Physics 19.3.3 Exponential Capacitor Discharge

Practise applying x = x0 exp(-t/RC) to capacitor current, charge or potential difference, rearranging it for time or circuit values and interpreting time constants.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • use x = x₀e^(−t/RC) for current, charge or potential difference during discharge
  • rearrange the exponential equation or use logarithms/ratios to determine time, RC or an initial quantity
  • interpret the value of the decaying variable at stated multiples of the time constant

19.3.3—Equations of the form x = x0 e–(t / RC) where x could represent current question 1

[Maximum number: 2]

A capacitor, a battery of electromotive force (e.m.f.) 12 V , a resistor R and a two-way switch are connected in the circuit shown in Fig. 5.1.

Fig. 5.1

Fig. 5.1

The switch is initially in position S . When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q.

The variation with t of ln⁡(Q/μC)\ln (Q / \mu C) is shown in Fig. 5.2.

Fig. 5.2

Fig. 5.2

A second identical resistor is now connected in parallel with R.

The switch is initially in position S . When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q.

On Fig. 5.2, sketch a line to show the variation of ln⁡(Q/μC)\ln (Q / \mu \mathrm{C}) with t between time t=0 and time t=5.0 st=5.0 \mathrm{~s}.

All question bank results loaded