RC Charging and Discharging Transients
For one equivalent resistance seen by a capacitor, tau = Rth C. Charging from zero toward Vfinal gives Vc = Vfinal(1-e^-t/tau); natural discharge gives Vc = V0 e^-t/tau.
Why this shows up in the exam
Capacitor charging time · Discharge from field or voltage data · Interpreting ln I versus time
Learn the idea
A first-order RC circuit approaches its final voltage exponentially with time constant RC. A capacitor voltage cannot jump instantly. During charging, current starts largest and decays; during discharge, stored voltage and current fall exponentially.
🧠 Memory hook: After one tau, the remaining gap is e⁻¹ of its old value.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau = R_th C — time constant using resistance seen by the capacitor
- V_C(t) = V_f + (V₀-V_f)e^(-t/tau) — general first-order capacitor response
- I(t) = I₀ e^(-t/tau) — natural exponential current magnitude in a simple RC transient
How to approach it
- 1Find V0 from the pre-switch circuit
- 2Find Vf and Rth from the post-switch circuit
- 3Use the general exponential and solve logarithms
Common slip-ups that cost marks
- •Using the visible resistor instead of Rth
- •Assuming capacitor voltage jumps
- •Confusing final value with the initial exponential amplitude
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
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