## Three phase AC circuits

## Topic

AC Circuit Fundamentals

Single phase AC Circuits

Three phase AC circuits

## AC Circuit Problems

- Two alternating currents in a parallel circuit are represented by i_1=5 sin(omega)t and i_2=10 sin((omega)t +60 deg). Find the resultant current.
- The equation for an AC voltage is given as v=0.04sin(2000t+60 degree)V. Determine the frequency, the angular frequency, instantaneous voltage when t=160 micro sec. What is the time represented by a 60 degree phase angle.
- Given v=200 sin 377t volts and i=8 sin(377t -30 degree) amperes for an AC circuit, determine (i) Power factor (ii) Power (iii) Apparent power (iv) Reactive power. Indicate the unit of power calculated.
- The instantaneous values of two alternating voltages are represented respectively by v_1= 60 sin theta volts and v_2=40 sin((theta-pi/3) volts. Calculate the (i) Sum & (ii) Difference of voltages.
- An alternating current i is given by i=100 sin 314 t. Find the (i) Amplitude (ii) Frequency (iii) Time period (iv) Form factor (v) Peak factor
- A parallel circuit consists of 20 ohms in series with an inductive reactance of 15 ohms in one branch and resistance of 30 ohms in series with a capacitive reactance of 20 ohms in the other branch. Determine the current and power dissipated in each branch if the total current drawn is 10 at an angle of (-30) degrees.
- For the current waveform shown in figure, find (i) Peak current (ii) Average current (iii) Periodic time (iv) Frequency (v) Instantaneous current at t=3 ms.

## Single Phase AC Circuit Problems

- A series RLC circuit is composed of a 100 ohms resistance, 1 H inductance and 5 micro farads capacitance. A voltage of v(t)=141.4 cos 377t volts is applied to the circuit, determine the current and voltages across resistance, inductance and capacitance.
- A series RLC circuit with 100 ohms, 25 micro farad and 0.15 henry is connected across 220 V, 50 Hz supply. Calculate (i) Impedance (ii) Current (iii) Power consumed (iv) Power factor of the circuit
- A coil of resistance 20 ohms and inductance of 0.0382 henry is connected in parallel to a circuit consisting of a 150 micro farad in series with a 10 ohms resistor. The arrangement is connected to a 230 V, 50 Hz supply. Determine current in each branch. Also find total supply current.
- A resistance of 7 ohms is connected in series with a pure inductance of 31.8 mH and the circuit is connected to a 100V, 50 Hz sinusoidal supply. Calculate (i) Circuit current (ii) Phase angle (iii) Power factor (iv) Power
- An alternating voltage of (160+j 120) V is applied to a circuit and the current is given by (6-j8) A. Find the values of circuit elements by assuming f=50 Hz. Calculate the power factor of the circuit and power consumed by the circuit.
- An inductive coil takes a current of 33.24 A from 230 V, 50 Hz supply, if the resistance of coil is 6 ohms. Calculate inductance of the coil and power taken by the coil.
- A coil of resistance 10 ohms and inductance of 0.1 H is connected in series with a 150 micro farad capacitor across a 200 V, 50 Hz supply. Calculate (i) Inductive reactance (ii) Capacitive reactance (iii) Impedance (iv) Current (v) Power factor (vi) Voltage across coil (vii) Voltage across capacitor.

## Three Phase AC Circuit Problems

- A Delta connected load consist of a resistance of 10 ohms and capacitance of 100 micro farad in each phase. A supply of 410 V at 50 Hz is applied to the load. Find line current, power consumed by the load and power factor
- A 3-phase load of 3 equal impedances are connected in delta across a balanced 400 V, 50 Hz, 3 phase supply which takes a line current of 10 A at a power factor of 0.7 lag. Calculate (i) Phase current (ii) Total Power in W (iii) Power in VA (iv) Power in VAR
- A balanced 3 phase star connected system draws power from 440 V supply. The two watt-meters connected indicate W1 = 5KW and W2 = 1.2 KW. Calculate power, power factor and current in the circuit
- 3 similar coils each having resistance of 10 ohms and reactance of 8 ohms are connected in star across 400 V, 3 phase supply. Determine (a) Line current (b) Total power (c) Reading of two watt-meters connected to measure power
- Three coils each of impedance 20∠60° Ω are connected in star to a 3 phase 400 V, 50 Hz supply. Find the reading on each of the two watt-meters connected to measure the power input.
- Two watt-meters are used to measure power in a 3-phase balanced load. The watt-meter readings are 2 KW and 7.5 KW. Calculate (i) Total Power (ii) Power factor (iii) Total reactive power
- Three coils are connected in delta to 3 phase, 3 wire 400 V, 50 Hz supply and takes a line current of 5A at 0.8 power factor lagging. Calculate the resistance and inductance of the coils