1. In an ideal capacitor connected to an alternating voltage source, the current leads the voltage by
A.
0°
B.
45°
C.
90°
D.
180°
Correct Answer:
90°
Explanation:
For an ideal capacitor in an AC circuit, the current leads the voltage by 90°.
2. The capacitive reactance of an ideal capacitor is given by
A.
X_C = 2πfC
B.
X_C = 1/(2πfC)
C.
X_C = C/(2πf)
D.
X_C = 2πC/f
Correct Answer:
X_C = 1/(2πfC)
Explanation:
The capacitive reactance is X_C = 1/(ωC) = 1/(2πfC).
3. If the frequency of the AC supply is increased, the capacitive reactance of an ideal capacitor
A.
Increases
B.
Decreases
C.
Remains unchanged
D.
Becomes infinite
Correct Answer:
Decreases
Explanation:
Since X_C = 1/(2πfC), capacitive reactance decreases when frequency increases.
4. For an ideal capacitor connected to an AC source, the average power consumed over one complete cycle is
A.
Maximum
B.
Zero
C.
Equal to the peak power
D.
Equal to the power of a resistor
Correct Answer:
Zero
Explanation:
The current and voltage in an ideal capacitor differ in phase by 90°, so the average power consumed is zero.
5. The rms current through an ideal capacitor connected to an AC voltage of rms value V is
A.
I = V/(ωC)
B.
I = VωC
C.
I = VC/ω
D.
I = Vω/C
Correct Answer:
I = VωC
Explanation:
For a capacitor, I = V/X_C. Using X_C = 1/(ωC), we get I = VωC.
6. An ideal capacitor offers maximum opposition to an AC current when the frequency of the supply is
A.
Zero
B.
Very low but nonzero
C.
Very high
D.
Equal to its capacitance
Correct Answer:
Zero
Explanation:
X_C = 1/(2πfC), so the capacitive reactance is greatest when the frequency approaches zero.
7. In an ideal capacitive AC circuit, the instantaneous current is related to the voltage by
A.
i = Cv
B.
i = C dv/dt
C.
i = v/C
D.
i = C/v
Correct Answer:
i = C dv/dt
Explanation:
The current through a capacitor is i = C dv/dt, where v is the instantaneous voltage.
8. If an ideal capacitor is connected to a DC source after the initial charging, the steady current through it is
A.
Zero
B.
Constant and maximum
C.
Alternating
D.
Infinite continuously
Correct Answer:
Zero
Explanation:
After an ideal capacitor becomes fully charged, the voltage stops changing, so dv/dt = 0 and the current becomes zero.
9. For a sinusoidal voltage v = V₀ sin(ωt) applied to an ideal capacitor, the current is
A.
i = ωCV₀ sin(ωt)
B.
i = ωCV₀ cos(ωt)
C.
i = V₀/(ωC) sin(ωt)
D.
i = V₀C cos(ωt)
Correct Answer:
i = ωCV₀ cos(ωt)
Explanation:
Using i = C dv/dt and differentiating v = V₀ sin(ωt), we obtain i = ωCV₀ cos(ωt).
10. The power factor of an ideal capacitive AC circuit is
A.
0
B.
1
C.
1/2
D.
Greater than 1
Correct Answer:
0
Explanation:
For an ideal capacitor, the phase difference between current and voltage is 90°, so the power factor cos 90° is zero.
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