Advertisements
Advertisements
Question
A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 300 μC. When potential across the capacitor is reduced by 100 V, the charge stored in it becomes 100 μC. Calculate The potential V and the unknown capacitance. What will be the charge stored in the capacitor if the voltage applied had increased by 100 V?
Advertisements
Solution
(i) Initial voltage, V1 = V volts, Charge stored,Q1 = 300 µC
Q1 = CV1 ..(1)
Changed potential, V2 = V-100 V
Q2 = 100 µC
Q2 = CV2 ..(2)
By dividing (2) from (1), we get `(Q_1)/(Q_2) = (CV_1)/(CV_2) => Q_1/Q_2 = V_1 /V_2`
`=> 300/100 = V/(V- 100) => V = 150 \text { volts }`
`∴ C = Q_1/V_1 = (300 xx 10^-6)/150 = 2 xx 10^-6 F = 2 μ F`
(ii) If the voltage applied had increased by 120 V, then V3 = 150+100 = 250 V
Hence, charge stored in the capacitor, Q3 = CV3 = 2×10-6×250 = 500 µC
(ii) If the voltage applied had increased by 120 V, then V3 = 150+100 = 250 V
Hence, charge stored in the capacitor, Q3 = CV3 = 2×10-6×250 = 500 µC
APPEARS IN
RELATED QUESTIONS
A bulb is connected in series with a variable capacitor and an AC source as shown. What happens to the brightness of the bulb when the key is plugged in and capacitance of the capacitor is gradually reduced?
Following operations can be performed on a capacitor:
X − connect the capacitor to a battery of emf ε.
Y − disconnect the battery.
Z − reconnect the battery with polarity reversed.
W − insert a dielectric slab in the capacitor.
(a) In XYZ (perform X, then Y, then Z) the stored electric energy remains unchanged and no thermal energy is developed.
(b) The charge appearing on the capacitor is greater after the action XWY than after the action XYZ.
(c) The electric energy stored in the capacitor is greater after the action WXY than after the action XYW.
(d) The electric field in the capacitor after the action XW is the same as that after WX.
Three capacitors having capacitances 20 µF, 30 µF and 40 µF are connected in series with a 12 V battery. Find the charge on each of the capacitors. How much work has been done by the battery in charging the capacitors?
Consider an assembly of three conducting concentric spherical shell of radii a, b and c as shown in figure Find the capacitance of the assembly between the points Aand B.
You are provided with 8 μF capacitors. Show with the help of a diagram how you will arrange minimum number of them to get a resultant capacitance of 20 μF.
A parallel plate capacitor stores a charge Q at a voltage V. Suppose the area of the parallel plate capacitor and the distance between the plates are each doubled then which is the quantity that will change?
The work done in placing a charge of 8 × 10–18 coulomb on a condenser of capacity 100 micro-farad is ______.
When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance ______.
The material filled between the plates of a parallel plate capacitor has a resistivity of 200Ωm. The value of the capacitance of the capacitor is 2 pF. If a potential difference of 40V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is ______.
(given the value of relative permittivity of a material is 50.)
Obtain the equivalent capacitance of the network shown in the figure. For a 300 V supply, determine the charge on each capacitor.
