Question 7: AC fundamentals

Question

A series R-C circuit is connected to 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 two
cases.

Accepted Answer

For circuit A
Impedence, $$Z_A=\sqrt{R^2+\frac{1}{\omega^2 c^2}}$$
Current in circuit $$I_R^A=\frac{V}{\sqrt{R^2+\frac{1}{\omega^2 c^2}}}$$ ..... (i)
Potential difference across $$C$$,
$$V_C^A=I_R^A 	imes \frac{1}{\omega c}=\frac{V}{\sqrt{(R \omega c)^2+1}}$$
For circuit B
Impedence, $$Z_B=\sqrt{R^2+\frac{1}{(4 \omega)^2 c^2}}$$
Current in circuit, $$I_R^B=\frac{V}{\sqrt{R^2+\frac{1}{(4 \omega c)^2}}}$$
Potential difference across $$C$$,
$$V_C^B=I_R^B 	imes \frac{1}{4 \omega c}=\frac{V}{\sqrt{(4 R \omega c)^2+1}}$$ ..... (ii)
Hence from above Eqs. (i) and (ii), we conclude that
$$I_R^B> I_R^A 	ext { and } V_C^A> V_C^B .$$

Answer

$$I_R^A> I_R^B$$

Answer

$$I_R^A< I_R^B$$

Answer

$$V_C^A< V_C^B$$

Answer

None of these

AC fundamentals

A series R-C circuit is connected to 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 two cases.

Choose the correct answer: