A series R-C circuit is connected to an AC voltage source. Consider two cases: (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current through the resistor and voltage across the capacitor are compar

Question

A series R-C circuit is connected to an AC voltage source. Consider two cases: (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current $I_{R}$ through the resistor and voltage $V_{C}$ across the capacitor are compared in the two cases. Which of the following is/are true? [2011]

Smart Achievers · Accepted Answer

(1, 3)

In an RC-circuit, the impedance is $Z = \sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}$

The capacitance in case B is four times the capacitance in case A

$∴$ Impedance in case B is less than that of case A $(Z_{B} < Z_{A})$

Now, $I = \frac{V}{Z},$

$∴$ $I_{R}^{A} < I_{R}^{B}$

and $V_{R}^{A} < V_{R}^{B}$ $\Rightarrow V_{C}^{A} > V_{C}^{B}$

[since, if V is the applied potential difference across the series RC circuit then $V = \sqrt{V_{R}^{2} + V_{C}^{2}}$ ]

Solution

1 $I_{R}^{A} > I_{R}^{B}$

2 $I_{R}^{A} < I_{R}^{B}$

3 $V_{C}^{A} > V_{C}^{B}$

4 $V_{C}^{A} < V_{C}^{B}$

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Solution

1 IRA>IRB

2 IRA<IRB

3 VCA>VCB

4 VCA<VCB

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1 $I_{R}^{A} > I_{R}^{B}$

2 $I_{R}^{A} < I_{R}^{B}$

3 $V_{C}^{A} > V_{C}^{B}$

4 $V_{C}^{A} < V_{C}^{B}$