Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainPhysicsAlternating Current

A parallel plate capacitor consists of two circular plates of radius R . The electric field between the plates varies with time t as E = E₀ ( t) . The RMS value of the conduction current in the connecting wires is :

Options

  1. A₀ E₀ R^2
  2. B₀ E₀ R^2 2
  3. C2 ₀ E₀ R^2
  4. D2 ₀ E₀ R

Correct answer

B. ₀ E₀ R^2 2

Step-by-step solution

The electric flux _E between the capacitor plates is the product of the electric field and the area of the plates: _E = E A = E₀ ( t) R^2 The displacement current I_d is defined as: I_d = ₀ d _E dt Substituting the expression for electric flux: I_d = ₀ R^2 d dt (E₀ ( t)) I_d = ₀ E₀ R^2 ( t) The peak value of the displacement current is the amplitude of this sinusoidal function: I₀ = ₀ E₀ R^2 By Maxwell's equations, the conduction current in the connecting wires is equal to the displacement current in the capacitor.

Practice Alternating Current on Quantrex Academy →

More from Alternating Current

Consider a circuit consisting of a capacitor of capacitance C and a coil with N turns per unit length, cross sectional area S and length d , where d^2 S . There is another coil of 2026An LCR series circuit driven with E_ rms = 90 V at frequency f_d = 30 Hz has resistance R = 80 , , an inductance with inductive reactance X_L = 20.0 , and capacitance with capacitiv 2026A series LCR circuit with R = 20 , L = 1.6 H and C = 40 F is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ . 2026An a.c. source of angular frequency is connected across a resistor R and a capacitor C in series. The current is observed as I . Now the frequency of the source is changed to /4 , 2026An inductor of 10 mH, capacitor of 0.1 F and a resistor of 100 are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5 . The d 2026The figure given below shows an LCR series circuit with two switches S₁ and S₂ . When switch S₁ is closed keeping S₂ open, the phase difference ( ) between the current and source v 2026An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. 2026The electric current in the circuit is given as i=i_ o (t / T) . The r.m.s current for the period t=0 to t=T is _ _ _ _ . 2026 Full Alternating Current list All JEE Main PYQs