Advertisements
Advertisements
Question
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
Solution 1
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
Solution 2
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
RELATED QUESTIONS
Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series−parallel connections.
Find the capacitances of the capacitors shown in figure . The plate area is Aand the separation between the plates is d. Different dielectric slabs in a particular part of the figure are of the same thickness and the entire gap between the plates is filled with the dielectric slabs.
Consider the situation shown in figure. The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.
If the voltage applied on a capacitor is increased from V to 2V, choose the correct conclusion.
Derive the expression for resultant capacitance, when the capacitor is connected in parallel.
Five capacitor each of capacitance value C are connected as shown in the figure. The ratio of capacitance between P to R, and the capacitance between P and Q is ______.
Consider two conducting spheres of radii R1 and R2 with R1 > R2. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.
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 ______.
