Problem 13
A 150-\(\Omega\) resistor is connected in series with a 0.250-H inductor and an ac source. The voltage across the resistor is \(v_R = (3.80 V)\)cos[720 rad/s)2t] . (a) Derive an expression for the circuit current. (b) Determine the inductive reactance of the inductor. (c) Derive an expression for the voltage \(v_L\) across the inductor.
Problem 14
You have a 200- resistor, a 0.400-H inductor, and a 6.00-F capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. (a) What is the impedance of the circuit? (b) What is the current amplitude? (c) What are the voltage amplitudes across the resistor and across the inductor? (d) What is the phase angle of the source voltage with respect to the current? Does the source voltage lag or lead the current? (e) Construct the phasor diagram
Problem 16
A 200-\(\Omega\) resistor, 0.900-H inductor, and 6.00-\(\mu\)F capacitor are connected in series across a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad>s. (a) What are \(v, v_R, v_L\), and \(v_C\) at \(t = 20.0 ms\)? Compare \(v_R + v_L + v_C\) to \(v\) at this instant. (b) What are VR , VL, and VC? Compare V to \(V_R + V_L + V_C\). Explain why these two quantities are not equal.
Problem 17
In an \(L-R-C\) series circuit, the rms voltage across the resistor is 30.0 V, across the capacitor it is 90.0 V, and across the inductor it is 50.0 V. What is the rms voltage of the source?
Problem 18
A resistor with \(R = 300\space \Omega\) and an inductor are connected in series across an ac source that has voltage amplitude 500 V. The rate at which electrical energy is dissipated in the resistor is 286 W. What is (a) the impedance Z of the circuit; (b) the amplitude of the voltage across the inductor; (c) the power factor?
Problem 19
The power of a certain CD player operating at 120 V rms is 20.0 W. Assuming that the CD player behaves like a pure resistor, find (a) the maximum instantaneous power; (b) the rms current; (c) the resistance of this player
Problem 20
In an \(L-R-C\) series circuit, the components have the following values: \(L = 20.0\space mH\), \(C = 140\space nF\), and R = 350 \(\Omega\). The generator has an rms voltage of 120 V and a frequency of 1.25 kHz. Determine (a) the power supplied by the generator and (b) the power dissipated in the resistor.
Problem 21
(a) Show that for an \(L-R-C\) series circuit the power factor is equal to R/Z. (b) An \(L-R-C\) series circuit has phase angle -31.5\(^\circ\). The voltage amplitude of the source is 90.0 V. What is the voltage amplitude across the resistor?
Problem 23
An \(L-R-C\) series circuit with \(L\) = 0.120 H, \(R\) = 240 \(\Omega\), and \(C\) = 7.30 \(\mu\)F carries an rms current of 0.450 A with a frequency of 400 Hz. (a) What are the phase angle and power factor for this circuit? (b) What is the impedance of the circuit? (c) What is the rms voltage of the source? (d) What average power is delivered by the source? (e) What is the average rate at which electrical energy is converted to thermal energy in the resistor? (f) What is the average rate at which electrical energy is dissipated (converted to other forms) in the capacitor? (g) In the inductor?
Problem 24
An \(L-R-C\) series circuit is connected to a 120-Hz ac source that has \(V_{rms} = 80.0 V\). The circuit has a resistance of 75.0 \(\Omega\) and an impedance at this frequency of 105 \(\Omega\). What average power is delivered to the circuit by the source?
