RC Circuits — Charging and discharging
Current Electricity
19
JEE Qs
8%
Hard
75
min
Master the initial (t=0+) and final (t=∞) states of the capacitor and how to correctly calculate the time constant (τ=RC) to efficiently solve most RC circuit problems.
🧮 Key Formulas
✅ Key Points for JEE
- 1At t=0 (just after connection), a capacitor acts like a short circuit to current. Its voltage cannot change instantaneously.
- 2At t=infinity (steady state), a capacitor acts like an open circuit for DC sources, blocking current completely, and its voltage equals the source voltage (if fully charged).
- 3The time constant τ = RC dictates the rate of charging/discharging. After one time constant (t=τ), the capacitor charges to approximately 63.2% of its final voltage or discharges to approximately 36.8% of its initial voltage.
- 4The behavior of voltage and current in RC circuits is exponential, governed by first-order differential equations derived from Kirchhoff's Voltage Law.
- 5For complex circuits, find the Thevenin equivalent resistance (R_eq) across the capacitor's terminals to correctly calculate the time constant: τ = R_eq * C.
⚠️ Common Mistakes
- ✕Incorrectly assuming capacitor voltage can change instantaneously at t=0; it's the current that's maximum at t=0.
- ✕Confusing the formulas for charging and discharging or misapplying initial/final conditions for voltage and current.
- ✕Calculating the equivalent resistance 'R' for τ incorrectly, especially in circuits with multiple resistors or sources.
- ✕Forgetting that the current through the resistor (and thus the voltage across it) starts high and decays to zero during charging, while the capacitor voltage builds up.
📝 Practice Questions
See allQ47.The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.
Q27.Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In the light of the above statements, choose the correct answer from the options given below. (1) Both Statement-I and Statement-II are false (2) Statement-I is false but Statement-II is true (3) Both Statement-I and Statement-II are true (4) Statement-I is true but Statement-II is false
Q34. Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance Rp = 1Ω as shown in the figure. An external resistance of Re = 2Ω is connected via the sliding contact. The electric current in the circuit is : (1) 0.9 A (2) 1.35 A (3) 0.3 A (4) 1.0 A 2025 (22 Jan Shift 1) JEE Main Previous Year Paper
Q45.Which of the following resistivity ( ρ ) v/s temperature (T) curves is most suitable to be used in wire bound standard resistors? (1) (2) (3) (4)
Q47.The net current flowing in the given circuit is_______ A.
Q30.Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of circuit is 6Ω B. Current in Ammeter is 1 A C. Potential across AB is 4 Volts. D. Potential across 2025 (23 Jan Shift 1) JEE Main Previous Year Paper CD is 4 Volts E. Total resistance of the circuit is 8Ω. Choose the correct answer from the options given below: (1) A, B and D Only (2) A, B and C Only (3) A, C and D Only (4) B, C and E Only
NCERT Chapters
- Class 12 Physics Ch 2: Electrostatic Potential and Capacitance
- Class 12 Physics Ch 3: Current Electricity