A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with acapacitance of 110 pF. When the frequency is doubled, the capacitance required for resonance is20 pF. The distributed capacitance of the coil in pico farad is _______.(Important - Enter only the numerical value in the answer)Correct answer is '10'. Can you explain this answer?

Question

Answer

Given information:
- Resonance at a frequency with capacitance 110 pF
- Resonance at double the frequency with capacitance 20 pF

To find:
- Distributed capacitance of the coil in pF

Solution:
Let L be the inductance of the coil and C be its distributed capacitance.
At resonance, the total capacitance C_tot is given by:

C_tot = C + C_m

where C_m is the capacitance of the Q-meter.

Let f be the resonant frequency of the coil.

At resonance, the impedance of the coil is purely resistive and is given by:

Z = R = √(L/C)

where R is the resistance of the coil.

When the frequency is doubled to 2f, the impedance of the coil becomes:

Z' = R' = √(L/(C + ΔC))

where ΔC is the change in the distributed capacitance due to the change in frequency.

Since the coil is still in resonance at 2f, we have:

Z' = R' = R

√(L/(C + ΔC)) = √(L/C)

Squaring both sides and simplifying, we get:

ΔC/C = 1/3

Therefore, the distributed capacitance of the coil is:

C = C_tot - C_m = 110 - 20 = 90 pF

So, the answer is 10 pF.

Therefore, the distributed capacitance of the coil is 10 pF.

Top Courses for GATE

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Other Engg Branches

Related Exams

Company