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?

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