Physics Alternating Current ETEA 2016
PMDC Verified Question 98 of 127
A \(35\ \mu\text{F}\) capacitor is connected to a source of sinusoidal e.m.f with a frequency of \(400\text{ Hz}\) and a maximum e.m.f of \(20\text{ V}\). The maximum current is:
A
0 A
B
0.28 A
C
1.8 A
D
230 A
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: 1.8 A
Concept:

Peak current through a capacitor is determined by peak voltage divided by capacitive reactance: \(I_0 = \omega C V_0 = 2\pi f C V_0\).

Formula / Reaction:

$$I_0 = 2\pi f C V_0$$

Solution:

  • Given: \(f = 400\text{ Hz}\), \(C = 35 \times 10^{-6}\text{ F}\), \(V_0 = 20\text{ V}\).


  • \(I_0 = 2 \times 3.1416 \times 400 \times (35 \times 10^{-6}) \times 20\).


  • \(I_0 = 2 \times 3.1416 \times 400 \times 700 \times 10^{-6} = 2 \times 3.1416 \times 0.28 \approx 1.76\text{ A} \approx 1.8\text{ A}\).


Why other options are incorrect:

  • Opt_A: Current is non-zero in an active AC circuit.


  • Opt_B: \(0.28\text{ A}\) misses multiplying by \(2\pi\).


  • Opt_D: Calculation error.

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