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The resonance frequency of a driven RLC circuit is 1300 Hz. a. What is the resonance frequency if the resistance R is doubled?
b. What is the resonance frequency if the inductance L is doubled?
c. What is the resonance frequency if the capacitance C is doubled?
d. What is the resonance frequency if the peak emf E_0 is doubled?
e. What is the resonance frequency if the emf frequency f is doubled?

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Karabo99

Answer:

a) f(R0) = 1000 Hz

b) f(R0) = 707.11 Hz

c) f(R0) = 707.11 Hz

d) f(R0) = 1000 Hz

e) f(R0) = 1000 Hz

Explanation:

Let R be the resistance of the circuit, L be the inductance of the circuit, C be the capacitance of the circuit, E_0 be the peak emf of the circuit, f be the frequency f(R) be initial resonance frequency of the circuit and f(R0) be the new respective resonance frequency in each question.

In an RCL circuit

f(R) = 1/2×π×√LC

a) f(R0) = 1000 Hz

The resonance frequency remains the same as it does not depend of resistance

b) f(R0) = 1/2×π×√2LC

f(R0)/1000 = √L/√2L

f(R0) = 7071 Hz

c) f(R0) = 1/2×π×√L2C

f(R0)/1000 = √C/√2C

f(R0) = 707.11 Hz

d)  f(R0) = 1000 Hz

The resonance frequency remains the same as it does not depend on the emf

e)   f(R0) = 1000 Hz

The resonance frequency remains the same as it does not depend of frequency

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