MHT CET · Physics · Alternating Current
When a.c. source is connected across a pure capacitor, the correct phase relation between current \(\left(\mathrm{i}_{\mathrm{c}}\right)\) and voltage \(\left(\mathrm{e}_{\mathrm{c}}\right)\) is shown in figure
- A (B)
- B (C)
- C (D)
- D (A)
Answer & Solution
Correct Answer
(A) (B)
Step-by-step Solution
Detailed explanation
Conceptual question. The current leads the voltage by \(\frac{\pi}{2}\) radians.
Ac voltage source, \(\mathrm{V}=\mathrm{V}_0 \sin (\omega \mathrm{t})\)
Charge at a given moment on the capacitor, \(\mathrm{q}=\mathrm{CV}\)
The current through the circuit: \(\frac{\mathrm{dq}}{\mathrm{dt}}=\left(\omega \mathrm{CV}_0\right)=\cos (\omega \mathrm{t})\)
As cos leads the \(\sin\) function by \(\frac{\pi}{2}\) radians.
Ac voltage source, \(\mathrm{V}=\mathrm{V}_0 \sin (\omega \mathrm{t})\)
Charge at a given moment on the capacitor, \(\mathrm{q}=\mathrm{CV}\)
The current through the circuit: \(\frac{\mathrm{dq}}{\mathrm{dt}}=\left(\omega \mathrm{CV}_0\right)=\cos (\omega \mathrm{t})\)
As cos leads the \(\sin\) function by \(\frac{\pi}{2}\) radians.
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