Advertisements
Advertisements
प्रश्न
Find the charge on each of the capacitors 0.20 ms after the switch S is closed in the figure.
Advertisements
उत्तर
The two 2.0 μF capacitors are in parallel, so Ceq = 2.0 + 2.0 = 4.0 μF.
With the 25 Ω series resistor and a 6.0 V battery:
τ = RC = (25) (4.0 × 10−6) = 1.0 × 10−4 s = 0.10 ms
At t = 0.20 ms = 2τ, the voltage across the capacitor bank is
VC(t) = V(1 − e−t/τ) = 6.0 (1 − e−2) ≈ 6.0 (0.8647) ≈ 5.19 V.
Each parallel capacitor has this same voltage, so the charge on each:
Q = CV = (2.0μF) (5.19V) ≈ 1.04 × 10−5C = 10.4μC.
APPEARS IN
संबंधित प्रश्न
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
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 energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?
Two capacitors of capacitances 4⋅0 µF and 6⋅0 µF are connected in series with a battery of 20 V. Find the energy supplied by the battery.
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.
Each capacitor in figure has a capacitance of 10 µF. The emf of the battery is 100 V. Find the energy stored in each of the four capacitors.
Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C1 as a function of time t.
Obtain the expression for the energy stored in a capacitor connected across a dc battery.
Choose the correct option:
Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
What fraction of the energy drawn from the charging battery is stored in a capacitor?
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)
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.
In a capacitor of capacitance 20 µF, the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, what is the new capacitance?
A parallel combination of two capacitors of capacities ‘C’ and ‘`C/3`’ respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is Q1, Q2 and E1, E2 respectively. Then the ratio of (E1 − E2) to (Q1 − Q2) is ______.
