Question

A changing voltage is applied to the clamps AB as mentioned in the diagram such that the voltage across the capacitor plates differs as mentioned in the figure. What will be the graph of time dependence of voltage across the clamps CD?

Answer 1

Hint: When the voltage across the capacitor is zero, the charge on it will also be zero. When the voltage of the capacitor is a constant, then the current will not be flowing through it. Analyse the graph given and find the voltage flow in each interval and find the corresponding graph. This all will help you in solving this question.

Complete answer:
From the figure we can see that during the interval of time from $0$ to ${{t}_{0}}$, ​the voltage across the capacitor will be zero, the charge on it will also be zero. Hence the current though this capacitor will be zero. Because of this, ${{U}_{CD}}$ ​will tend to be zero during this interval of time as mentioned in the figure. During the time interval from \[{{t}_{0}}\] ​ and \[2{{t}_{0}}\], we can see that​ the voltage across the capacitor, and as a result of this, the charge on its plates are growing linearly. Therefore a direct current will be passing through the circuit. This means that the voltage ${{U}_{CD}}$ ​ is a constant. In the interval of time from \[2{{t}_{0}}\]to \[3{{t}_{0}}\]​, the voltage across the capacitor will be a constant. Therefore the current will not be flowing and ${{U}_{CD}}$ will be zero. And at last during the time interval from \[3{{t}_{0}}\]​ to \[5{{t}_{0}}\]​, the capacitor will be discharged, the current through the resistor will be a negative and constant, and also its magnitude will be the half the value of current during the time interval from \[{{t}_{0}}\] to \[2{{t}_{0}}\].

 Therefore the graph has been obtained.

Note:
A capacitor is a device which is used in order to store the electric field. This energy is being stored between two metal plates which are separated by a distance containing a specific dielectric medium in between the metal plates. This device can operate only in the presence of alternate current.