Question

A Capacitor of \[2\mu F\] is connected in a radio circuit. The source frequency is $1000\,Hz$. If the current through the capacitor branch is \[2mA\] then voltage across the capacitor is
A. 0.16 V
B. 0.32 V
C. 156 V
D. 79.5 V

Answer 1

Hint: In the question above capacitance , frequency and current has been given. By ohm’s law we know that voltage is directly proportional to current and \[V = iR\]. In this case. First we find the capacitive reactance \[{\chi _c}\] and then we find the voltage $V$.

Formula used:
\[V = i\dfrac{1}{{\omega C}}\]
where \[{\chi _c}\]=capacitive reactance.

Complete step by step answer:
We know that AC is alternating current which periodically reverses its direction unlike DC. AC is generally used for distribution of power .By ohm’s law we know that,
$V=IR$…………....(I=current, V=voltage ,R=resistor)

As this is an AC circuit the voltage will be given by \[V = i{\chi _c}\].Capacitive reactance Is the opposition offered by capacitor to the change in voltage across the element. Look at the diagram below :

We are suppose to find the voltage ;
We know that:
\[{\chi _c} = \dfrac{1}{{\omega C}}\] (where \[\omega = \]frequency)
Substituting the values of C, \[\omega \] and we get:
\[V = \dfrac{{2 \times {{10}^{ - 2}}}}{{2\pi \times 1000 \times 2 \times {{10}^{ - 6}}}}\]
\[V = 0.16\,V\]
Hence after solving we see that voltage =0.16 V.

Therefore the correct answer is option A.

Additional information: For a purely capacitive AC circuit, instantaneous value of current is given by: \[i = \left( {\dfrac{{{V_0}}}{{\dfrac{1}{{\omega C}}}}} \right)\cos \omega t\]
\[i = {i_0}\sin \left( {\omega t + \phi } \right)\]. This equation tells us that the current leads voltage by \[\left( {\dfrac{\pi }{2}} \right)\].

Note: The capacitive reactance is given by \[{\chi _c} = \dfrac{1}{{\omega C}}\] and inductive reactance is given by \[{\chi _L} = \omega L\].do not get confused with the formulas. In a pure capacitive circuit current always leads the voltage by \[{90^ \circ }\] and average power applied to it is zero. The capacitive reactance increases with decrease in frequency.