Question

A capacitor is connected in an electric circuit. When key is pressed, the current in the circuit is:
A. zero
B. maximum
C. any transient value
D. depends on capacitor used

Answer 1

Hint: When a fully charged capacitor with capacitance C is connected in an electric circuit containing resistor R and key is pressed, the capacitor starts discharging. Initially the current in the circuit is maximum but it decreases with time and finally becomes Zero.

Complete step by step answer:
When a fully charged capacitor with capacitance C is connected in an electric circuit containing resistor R, then the current in a circuit in the circuit during discharging is given by the relation
\[{I_c} = {I_0}{e^{\dfrac{{ - t}}{\tau }}}\], where \[{I_c}\] is the current during any instant of time t, \[{I_0}\]is the maximum current flowing through the circuit and is given at \[t = 0\], R is the resistance of the resistor in ohms and \[\tau \] is the time constant and is given by the relation \[\tau = RC\]. It is also known as the RC factor.
When the key is just pressed, that is at t = 0, we have \[{e^{\dfrac{{ - 0}}{\tau }}} = 1\]. Putting this value in the relation \[{I_c} = {I_0}{e^{\dfrac{{ - t}}{\tau }}}\] , we get \[{I_c} = {I_0}\]. Hence the current will be maximum when the key is pressed in an electric circuit containing a capacitor.

Note:An electric circuit containing a resistance and a capacitor is known as a RC circuit. There is a growth and decay of current that takes place in a RC circuit and the current in the circuit is determined by the factor \[\tau \] known as the time constant of RC factor. The current in the circuit varies exponentially between the time , \[t = 0\] to \[t = t.\]