The value of the rms current if the frequency of the supply is changed to 60.0 Hz.
Answer to Problem 82QAP
If the frequency of the supply is changed to 60.0 Hz, the rms current flowing in the circuit is 57.3 mA.
Explanation of Solution
Given info:
Capacitance of the capacitor
Voltage amplitude
Resonant frequency
Maximum rms current
New frequency
Formula used:
When the current flowing in a RLC circuit connected to an ac supply is maximum, the frequency of the source is equal to Resonant frequency. When the circuit is in resonance, the impedance of the circuit is purely resistive. Therefore, the resistance R of the RLC circuit is given by,
Where, the rms voltage is given by,
Therefore,
The resonant frequency is related to the inductance L and the capacitance C as follows:
Rewrite the equation for L.
Using the values of L and R calculated using equations (1) and (2) the impedance Z of the circuit at a frequency f can be calculated using the expression:
The rms current flowing in the circuit at a frequency f is given by,
Calculation:
Calculate the resistance R of the circuit by substituting the known values of the variables in equation (1).
Calculate the inductance of the circuit by substituting the known values of the variables in equation (2).
Calculate the value of impedance of the circuit at a frequency 60.0 Hz by substituting the known values of the variables in equation (3).
Finally determine the rms value of current flowing in the circuit at the frequency 60.0 Hz by substituting the values of the variables in equation (4).
Conclusion:
Thus, if the frequency of the supply is changed to 60.0 Hz, the rms current flowing in the circuit is 57.3 mA.
Want to see more full solutions like this?
Chapter 21 Solutions
COLLEGE PHYSICS
- Calculate the rms currents for an ac source is given by v(t)=v0sint , where V0=100V and =200rad/s when connected across (a) a 20F capacitor, (b) a 20-mH inductor, and (c) a 50 resistor.arrow_forwardThe emf of an ac source is given by v(t)=v0sint. where V0=100V and at =200rad/s . Calculate the average power output of the source if it is connected across (a) a 20F capacitor, (b) a 20-mH inductor, and (c) a 50 resistor.arrow_forwardA 20-mH inductor is connected across an AC source with a variable frequency and a constant-voltage amplitude of 9.0 V. (a) Determine the reactance of the circuit and the maximum current through the inductor when the frequency Is set at 20 kHz. (b) Do the same calculations for a frequency of 60 Hz.arrow_forward
- The emf of an ac source is given by v(t)=V0sint, where V0=100V and =200 . Find an expression that represents the output current of the source if it is connected across (a) a 20-pF capacitor, (b) a 20-mH inductor, and (c) a 50 resistor.arrow_forwardAt 1000 Hz, the reactance of a 5.0-mH inductor is equal to the reactance of a particular capacitor. What is the capacitance of the capacitor?arrow_forwardWhat is the impedance of a series combination of a 50resistor, a 5.0F capacitor, and a 10F capacitor at a frequency of 2.0 kHz?arrow_forward
- A 700-pF capacitor is connected across an ac source with a voltage amplitude of 160 V and a frequency of 20 kHz. (a) Determine the capacitive reactance of the capacitor and the amplitude of the output current of the source. (b) If the frequency is changed to 60 Hz while keeping the voltage amplitude at 160 V, what are the capacitive reactance and the current amplitude?arrow_forwardThe resonant frequency of RLC series circuits is 2.0103Hz , If the self-inductance in the circuit is 5.0 mH, what is the capacitance in the circuit?arrow_forwardAn ac source of voltage amplitude 10 V delivers electric energy at a rate of 0.80 W when its current output is 2.5 A. What is the phase angle between the emf and the current?arrow_forward
- In a series RLC circuit with a maximum current of 0.250 A, an AC source with Vmax= 115 V operating at 60.0 Hz is connected to a 325-mH inductor, a 7.50-F capacitor, and a resistor with unknown resistance R. Draw a phasor diagram for this circuit, including the current, the potential difference across each of the circuit elements, and the source emf. Draw your diagram with the current phasor pointing upward along the vertical axis.arrow_forwardAn PLC series circuit with R=600 , L = 30 mH. and c=0.050F is driven by an ac source whose frequency and voltage amplitude are 500 Hz and 50 V, respectively, (a) What is the impedance of the circuit? (b) What is the amplitude of the current in the circuit? (c) What is the phase angle between the emf of the source and the current?arrow_forwardIn an ideal AC circuit with capacitance, there is no resistance. Is any energy dissipated? How about in a real AC circuit with capacitance?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill