In the circuit shown,R = 100 W,L = 50 mH,C = 10 mF,and the ideal AC emf source has a peak voltage of 120V.What angular frequency $\omega$ should be used to produce the largest current in the resistor?
A)6.3 rad/s
B)22 rad/s
C)45 rad/s
D)2000 rad/s
E)13000 rad/s

Question

In the circuit shown,R = 100 W,L = 50 mH,C = 10 mF,and the ideal AC emf source has a peak voltage of 120V.What angular frequency $\omega$ should be used to produce the largest current in the resistor? 
A)6.3 rad/s 
B)22 rad/s 
C)45 rad/s 
D)2000 rad/s 
E)13000 rad/s

Quizplus · Accepted Answer

The impedance of the circuit is given by:
Z = R + j(XL - XC)
where XL is the inductive reactance and XC is the capacitive reactance. 
XL = 2πfL and XC = 1/(2πfC)

At resonance, XL = XC, so we have:
2πfL = 1/(2πfC)
Solving for f, we get:
f = 1/(2π√(LC))

Substituting the given values, we get:
f = 45.16 Hz = 2π(45) rad/s

Therefore, the best choice is C) 45 rad/s, as this frequency will make the impedance purely resistive, maximizing the current through the resistor.

In the Circuit Shown,R = 100 W,L = 50 MH,C ω\omegaω

In the Circuit Shown,R = 100 W,L = 50 MH,C $\omega$