LCR Circuits: Phase difference between voltage and current.

Given that R=1 kilo ohm, C= 1micro farad and L= 100 milli Henry’s calculate the frequency at which the current in an LCR series circuit lags the supply voltage by 45 degrees.

Calculating current, impedance and voltage in a circuit in polar form

Full question attached as a file Calculate values of I1, I2, I3, V1, Vs and total impedance in circuit shown, giving answers in polar form using V2 as the reference. I have calculated the following and think they are correct: I1=1.01 I2=1 I3=1.43 V1=2.02 Vs=2.93 I am lost with the polar form using V2 as a reference and stumped on question B Can you show answers and explanations so I can work my way through

Magnitude of ac input

Magnitude of ac input. See attached file for full problem description.

Solid State Device Theory Exercise

Solid State Device Theory Exercise. See attached file for full problem description.

Power factor in AC circuit

A single phase electric motor has an output power of 10 kW and an efficiency of 90% at full load. The motor is fed from a 240 V supply via a cable that has a resistance of 10 milli ohms per metre length. If the terminal voltage to the motor must not fall below 90% of the supply voltage, calculate the maximum return length of the cable for a motor power factor of: A. unity B. 0.8 (sketch a circuit diagram and phasor diagram, the motor and line voltages are no longer in phase) C. The power dissipated in the cable for each of the above two cases.