Question

A series R-C circuit is connected to an alternating voltage source. Consider two situations:
(a) When capacitor is filled
(b) When capacitor is mica filled
Current through resistor is I and voltage across capacitor is V then:
A. \[{V_a} = {V_b}\]
B. ${V_a} < {V_b}$
C. ${V_a} > {V_b}$
D. ${i_a} = {i_b}$

Answer 1

Hint: Here we can use the impedance formula:
                     \[Z = \sqrt {{R^2} + {X_C}^2} \]

Complete step by step answer:
Let us consider the first case when the capacitor is filled,
In case of a C-R series circuit, the impedance is calculated by the formula,
  \[Z = \sqrt {{R^2} + {X_C}^2} \]
Where,
\[{X_c}\] is the measure of opposition to the alternating current. It is known as Effective capacitance and the effective capacitance is inversely proportional to the reactance.
\[{X_c} = \dfrac{I}{{{\omega _c}}}\]
\[I = \dfrac{v}{z}\]
 Now let us consider the second case when the capacitor is filled with mica, the capacitance of the capacitor increases. As a result, if C increases, then the value of\[{X_C}\]decreases and causes an increase in current. Thus, the voltage across the capacitor decreases, and the voltage across resistance increases.
We then can conclude that \[{V_a} > {V_b}\]
Hence, the option (C) is the correct answer.

Additional Information: Electrical impedance is a measure of opposition presented by a circuit to the current when a specific voltage is applied. In other words, impedance is a complex ratio of voltage to current in an AC (alternating current) circuit. An LCR circuit is made up of an inductor having inductance L, a resistor with a resistance of R, and a capacitor with a capacitance of C. The inductance, resistor and capacitor are all connected in series, ensuring that the same current amount passes through each. For the resistor, the current I and the voltage are said to be in phase. For an inductor, the current I lag behind voltage by 90. For a capacitor, current I lead voltage by 90. The resistance provided by the inductor is called inductive reactance and the resistance provided by the capacitor is known as capacitive reactance.

Note: It is important to note that in the impedance formula, the square root covers both R and, and both these values are squared separately.