Advertisements
Advertisements
प्रश्न
The variation of inductive reactance (XL) of an inductor with the frequency (f) of the ac source of 100 V and variable frequency is shown in fig.
- Calculate the self-inductance of the inductor.
- When this inductor is used in series with a capacitor of unknown value and a resistor of 10 Ω at 300 s–1, maximum power dissipation occurs in the circuit. Calculate the capacitance of the capacitor.
Advertisements
उत्तर १
i. We know that XL = ωL and ω = 2π f
Where,
f = frequency in Hz
So, L = `X_L/(2 pi f)`
= `(20)/(2 pi(100))`
= `(40)/(2pi (200))`
= `(60)/(2pi(300))`
= 31.84 × 10−3
≈ 32 mH
ii. We know that power dissipation is maximum when,
XL = XC
⇒ ωL = `1/(omegaC)`
⇒ `C = 1/(omega^2L)`
⇒ C = `1/(4 pi^2 f^2 L)`
= `1/(4 xx 3.14 xx 3.14 xx 300 xx 300 xx 32 xx 10^-3)`
= 8.8 μF
उत्तर २
i. Given: From graph f = 100 Hz
XL = 20 Ω
Inductive reactance (XL) = 2π f L
So,
L = `X_L/(2 pi f)`
= `(20)/(2 pi xx 100)`
= 0.032 H
= 32 mH
ii. Given: f = 300 s−1
L = 0.032H
We know that power dissipation is maximum when,
2π f L = `1/(2 pi f C)`
2π × 300 × 0.032 = `1/(2 pi xx 300 xx C)`
∴ C = 8.8 × 10−6 F
= 8.8 μF
संबंधित प्रश्न
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?
A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (a) The electric field between the plates of the capacitor Justify your answer by writing the necessary expressions.
A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
The equivalent capacitance of the combination shown in the figure is _________ .
Find the charges on the three capacitors connected to a battery as shown in figure.
Take `C_1 = 2.0 uF , C_2 = 4.0 uF , C_3 = 6.0 uF and V` = 12 volts.
Each of the capacitors shown in figure has a capacitance of 2 µF. find the equivalent capacitance of the assembly between the points A and B. Suppose, a battery of emf 60 volts is connected between A and B. Find the potential difference appearing on the individual capacitors.
A finite ladder is constructed by connecting several sections of 2 µF, 4 µF capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C, such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between?
Three capacitors C1 = 3μF, C2 = 6μF, and C3 = 10μF are connected to a 50 V battery as shown in Figure below:
Calculate:
(i) The equivalent capacitance of the circuit between points A and B.
(ii) The charge on C1.
A capacitor has charge 50 µC. When the gap between the plate is filled with glass wool, then 120 µC charge flows through the battery to capacitor. The dielectric constant of glass wool is ______.
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
