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
Two identical parallel plate capacitors A and B are connected to a battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.
Take `C_1 = 4.0 "uF" and C_2 = 6.0 "uF"` in figure . Calculate the equivalent capacitance of the combination between the points indicated.
Find the charge supplied by the battery in the arrangement shown in figure.
A capacitor is formed by two square metal-plates of edge a, separated by a distance d. Dielectrics of dielectric constant K1 and K2 are filled in the gap as shown in figure . Find the capacitance.
Figure shows two parallel plate capacitors with fixed plates and connected to two batteries. The separation between the plates is the same for the two capacitors. The plates are rectangular in shape with width b and lengths l1 and l2. The left half of the dielectric slab has a dielectric constant K1 and the right half K2. Neglecting any friction, find the ration of the emf of the left battery to that of the right battery for which the dielectric slab may remain in equilibrium.
- Charge on each capacitor remains same and equals to the main charge supplied by the battery.
- Potential difference and energy distribute in the reverse ratio of capacitance.
- Effective capacitance is even les than the least of teh individual capacitances.
Can the potential function have a maximum or minimum in free space?
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
Calculate equivalent capacitance of the circuit shown in the Figure given below:
Eight drops of mercury of equal radius and possessing equal charge combine to form a big drop. The capacitance of bigger drop as compared to each small drop is ______.
