Advertisements
Advertisements
Question
A capacitor of capacitance 500 μF is connected to a battery through a 10 kΩ resistor. The charge stored in the capacitor in the first 5 s is larger than the charge stored in the next.
(a) 5 s
(b) 50 s
(c) 500 s
(d) 500 s
Advertisements
Solution
(a) 5 s
(b) 50 s
(c) 500 s
(d) 500 s
The charge (Q) on the capacitor at any instant t,
\[Q = CV(1 - e^{- t/RC} )\]
where
C = capacitance of the given capacitance
R = resistance of the resistor connected in series with the capacitor
RC = (10 × 103) × (500 × 10-6) = 5 s
The charge on the capacitor in the first 5 seconds,
\[Q_0 = CV(1 - e^{- 5/5} ) = CV \times 0 . 632 \]
The charge on the capacitor in the first 10 seconds,
\[Q_1 = CV(1 - e^{- 10/5} )\]
\[ Q_1 = CV(1 - e^{- 2} ) = 0 . 864 \times CV\]
Charge developed in the next 5 seconds,
Q' = Q1 - Q0
Q' = CV(0.864 - 0.632) = 0.232 CV
The charge on the capacitor in the first 55 seconds,
\[Q_2 = CV(1 - e^{- 55/5} )\]
\[ Q_2 = CV(1 - e^{- 11} ) = 0 . 99 \times CV\]
Charge developed in the next 50 seconds,
Q' = Q2 - Q0
Q' = CV(0.99 - 0.632) = 0.358 CV
Charge developed in the first 505 seconds,
\[Q_3 = CV(1 - e^{- 500/5} ) = CV(1 - e^{- 100} ) \approx CV\]
Charge developed in the next 500 seconds,
Q' = CV (1 - 0.632) = 0.368 CV
Thus, the charge developed on the capacitor in the first 5 seconds is greater than the charge developed in the next 5,50, 500 seconds.
Notes
Out of the four given options, two options are same.
APPEARS IN
RELATED QUESTIONS
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
In the following arrangement of capacitors, the energy stored in the 6 µF capacitor is E. Find the value of the following :
(i) Energy stored in 12 µF capacitor.
(ii) Energy stored in 3 µF capacitor.
(iii) Total energy drawn from the battery.
Find the charge on the capacitor as shown in the circuit.
Find the ratio of energy stored in the two configurations if they are both connected to the same source.
A capacitor C1 of capacitance 1 μF and a capacitor C2 of capacitance 2 μF are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t = 0.
(a) The current in each of the two discharging circuits is zero at t = 0.
(b) The currents in the two discharging circuits at t = 0 are equal but not zero.
(c) The currents in the two discharging circuits at t = 0 are unequal.
(d) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.
Find the charge on the capacitor shown in the figure.
How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.
A capacitor of capacitance C is connected to a battery of emf ε at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate have this maximum value?
A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫ i2R dt and also by finding the decrease in the energy stored in the capacitor.
A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an ideal battery of emf ε through a resistance R. Find the charge on the capacitor at time t.
A metal sphere of radius R is charged to a potential V.
- Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
- Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.
A parallel plate capacitor has a uniform electric field ‘`vec "E"`’ in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is ______
(ε0 = permittivity of free space)
A parallel plate capacitor has a uniform electric field `overset(->)("E")` in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is ______
(ε0 = permittivity of free space)
Do free electrons travel to region of higher potential or lower potential?
Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must be intermediate in potential between that of the charged body and that of infinity.
Derive an expression for energy stored in a capacitor.
