Question

In: Physics

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The...

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε =V_a - V_b = ε_msinωt, where ε_m = 120 V and ω = 231 radians/second. The inductance L = 155 mH. The values for the capacitance C and the resistance R are unkown. What is known is that the current in the circuit leads the voltage across the generator by φ = 49 degrees and the average power delivered to the circuit by the generator is P_avg = 106 W.

What is I_max, the amplitude of the current oscillations in the circuit?

What is R, the value of the resistance of the circuit?

What is C, the value of the capacitance of the circuit?

The value of ω is now changed, keeping all other circuit parameters constant, until resonance is reached. How was ω changed?

ω was decreased

ω was increased

What is the average power delivered to the circuit when it is in resonance?

Expert Solution

Solution :

part a : Determination of I_max :

part b : Determination of the value of Resistor, R:

Part c: Determination of value of Capacitance,C:

Hence, C = 27.03 and
C = 60.58

Part d:

When the current is lagging behind the voltage, the capacitance,C of the circuit must increase in order to reach resonance.

where ω is decreasing.

When the current is leading the voltage, the inductance of the circuit, L must increase in order to reach resonance.

where, ω is increasing.

Part e : Determination of average power :

genius_generous answered 1 year ago

a circuit that has a resistor, capacitor, and inductor in series with a 5V AC voltage...

a circuit that has a resistor, capacitor, and inductor in series with a 5V AC voltage source R = 5 Ω; L = 1 mH; C = 447 a) Find ω0 and f0 b) Complete the table f = f0 f = 0.5f0 f = 1.5f0 I VL Vc c) What is the phase between circuit current and applied voltage at f = f0 (in radians) d) Determine if the below statements are true or false Below resonance (f <...

A series AC circuit contains a resistor, an inductor of 240 mH, a capacitor of 5.40...

A series AC circuit contains a resistor, an inductor of 240 mH, a capacitor of 5.40 µF, and a source with ΔVmax = 240 V operating at 50.0 Hz. The maximum current in the circuit is 170 mA. (a) Calculate the inductive reactance. _________________Ω (b) Calculate the capacitive reactance. ______________-Ω (c) Calculate the impedance. _______________kΩ (d) Calculate the resistance in the circuit. ______________kΩ (e) Calculate the phase angle between the current and the source voltage. _______________°

10.An AC voltage source is connected in series to an inductor, a capacitor, and a resistor...

10.An AC voltage source is connected in series to an inductor, a capacitor, and a resistor of 8 Ohms. At the frequency when the phase angle is zero, capacitive reactance is 7 Ohms. What is the phase angle between the current and voltage at a frequency which is a factor of 3.2 times less than this frequency? answer in degresss and if negative 6. the resistance of a coil spun in a generator is 2 Ohms. the coil is in...

A circuit is consisted of an inductor L, a capacitor C, and a resistor R. It...

A circuit is consisted of an inductor L, a capacitor C, and a resistor R. It is driven by an AC voltage of the form ?0sin (??). At the steady state, find (a) the charge and current as a function of time (b) the maximum amplitude of the current and the corresponding resonance frequency (c) the average power at the current’s resonance frequency (c) the quality factor Q

A resistor, inductor, and capacitor are connected in parallel with a function generator. Calculate the apparent...

A resistor, inductor, and capacitor are connected in parallel with a function generator. Calculate the apparent power of the circuit. Enter your answer in VA but do not enter the unit. Round to the nearest whole VA. VT = 117V RMS, R = 170Ω, XL = 169Ω, XC = 46Ω

Suppose an electrical circuit contains a 1 H inductor, a 10 Ω resistor and a capacitor...

Suppose an electrical circuit contains a 1 H inductor, a 10 Ω resistor and a capacitor rated at 1/7 F. If the circuit is hooked up to an alternating voltage source described by E(t) = 68 cost V and initially q(0) = 1 C and i(0) = 0 A, find a function that describes the charge as a function of time. Lq'' + Rq' + q/C = E(t). Please show work using a complementary and particular solution if possible.

A series ac circuit contains a 210 Ω resistor, a 20.0 mH inductor, a 3.30 μF...

A series ac circuit contains a 210 Ω resistor, a 20.0 mH inductor, a 3.30 μF capacitor, and an ac power source of voltage amplitude 45.0 V operating at an angular frequency of 360 rad/s . 1)What is the power factor of this circuit? 2)Find the average power delivered to the entire circuit. 3)What is the average power delivered to the resistor, to the capacitor, and to the inductor?

An RLC series circuit has a 2.60 ? resistor, a 200 µH inductor, and a 78.0 µF capacitor.

An RLC series circuit has a 2.60 ? resistor, a 200 µH inductor, and a 78.0 µF capacitor. (a) Find the circuit's impedance (in ?) at 120 Hz. (b) Find the circuit's impedance (in ?) at 5.00 kHz. (c) If the voltage source has Vrms = 5.60 V, what is Irms (in A) at each frequency? Irms, 120 Hz =_____ A Irms, 5.00 kHz =_____A (d) What is the resonant frequency (in kHz) of the circuit? (e) What is...

A circuit is constructed with four resistors, one inductor, one battery and a switch as shown....

A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 56 Ω, R3 = 45 Ω and R4 = 91 Ω. The inductance is L = 255 mH and the battery voltage is V = 24 V. 1) The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the...

A circuit is constructed with four resistors, one capacitor, onebattery and a switch as shown....

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 32 Ω, R3 = 90 Ω and R4 = 89 Ω. The capacitance is C = 85 μF and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.1) The switch has been open for a long time when at time t = 0,...