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A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360μC. When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120μC.
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Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by120 V?

Answer
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Hint: This numerical problem can be solved by using the fact that value of the capacitance is actually determined only by the physical characteristics of the capacitor. This is because according to the principle of a capacitor, its capacitance increases only when the voltage decreases. We can use this expression to solve this numerical problem.

Formula Used:
We know that capacitance is actually the ratio of charge and potential. This can be mathematically represented by the mathematical expression given below:
C=Q/V
We will use the above mathematical expression to solve the given numerical problem.

Complete step by step answer:
First we will have to consider the initial voltage of the capacitor to be V1=V. Now, the initial charge of the capacitor is given in the numerical problem as q1=360μC.
Now, using these values in the expression for capacitance of the conductor, we get:
C=q1V1=360V
Now, according to the question, the voltage is reduced by 120 V thus, V2=V120. The charge on the capacitor is now equal to 120μC.
Now, we will again find the capacitance by using the formula given above:
Thus, C=q2V2=120(V120)
Now, we can say that the capacitance of the capacitor remains constant as there is no change in area of the plates, medium and distance between plates. Thus, we can equate the value of the capacitance from both the equations. Thus,
360V=120(V120)
Using V as the subject of the formula, we get:
3(V120)=V
Solving for V we have:
V=3602=180V
Now, we can use this value of the potential to obtain the unknown capacitance by substituting this in the above formula:
C=130180=2μF
Thus, the answer to (i) is that the potential is equal to 180V and the unknown capacitance is equal to 2μF.
Now, it is given that the voltage applied is increased by 120V. Thus, we have to add this increase in voltage to the original potential. Thus,
New voltage, V=180+120=300V
Now, the charge stored in a capacitor is given by the mathematical formula q=CV. Thus, substituting these values in the equation, we get:
q=2×300=600μC
Thus the answer for (ii) is equal to 600μF.

Note: It is important to proceed in a step by step manner while solving numerical problems related to capacitance. Students usually get confused while working on such numerical problems as there are many increases and decreases in currents and voltages which might confuse them.