Question

A $50Hz$ AC source of $20V$ is connected across R and C as shown in figure below. The voltage across R is $ 12V $ . The voltage across C is
A) $8V $
 B) $16V $
 C) $10V $
 D) Not possible to determine unless values of R and C are given.

Answer 1

Hint: This question is based on the concept of RC circuit. This can be considered a special case of an LCR circuit. A resistor–capacitor circuit, or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses.

Complete step by step solution:
RC circuits are a frequent element in electronic devices. They also play an important role in the transmission of electrical signals in nerve cells. A capacitor can store energy and a resistor placed in series with it will control the rate at which it charges or discharges.
The RC circuit is used in camera flashes, pacemaker, timing circuit etc. The RC signal filters the signals by blocking some frequencies and allowing others to pass through it. It is also called first-order RC circuit and is used to filter the signals bypassing some frequencies and blocking others.
Given,
Source Voltage $ {V_s} = 20V $ and Voltage across the resistor $ {V_r} = 12V $
For an AC R-C circuit,
 $ V_s^2 = V_r^2 + V_c^2 $
This can be rewritten as,
 $ V_c^2 = V_s^2 - V_r^2 $
On taking square root on both the sides, we get,
 $ {V_c} = \sqrt {V_s^2 - V_r^2} $
On substituting the given values,
 $ {V_c} = \sqrt {{{(20)}^2} - {{(12)}^2}} $
 $\Rightarrow {V_c} = \sqrt {400 - 144} $
On simplification,
 $ \Rightarrow {V_c} = \sqrt {256} $
On simplifying the root,
 $ {V_c} = 16V $
Therefore, The voltage across $C$ is $16V$. So, option (B) is correct.

Note:
The RC circuit has thousands of uses and is a very important circuit to study. Not only can it be used to time circuits, it can also be used to filter out unwanted frequencies in a circuit and used in power supplies, like the one for your computer, to help turn ac voltage to dc voltage.