Question

If a 120 V (rms) AC power supply is connected to a 200 W motor.

a)Calculate and explain whether or not the rms current of the circuit will be the same if the system is connected to a 14.0Ω resistor.

(I need a clear explanation in b))

b)Calculate and explain whether or not the rms voltage drop across the motor is the same when there is no resistor, but the internal resistance of the wires of the circuit is 14.0Ω.

Answer 1

a) The power consumed by the motor when connected to an AC power supply is given by,

P=VI where V= potential difference across the motor ; I= current through the motor

Here, V_rms= 120 V then I_rms= P / V = (200 / 120) A = 1.67 A

Since this is series circuit, the same current flows through the circuit. Hence the current through the circuit is 1.67 A

On the other hand, if the same AC power supply is connected to a 14 Ω resistor then the current in the circuit is given by,

V=IR where I = current through the circuit ; R = Resistance of the circuit

Thus I_rms = V_rms / R = (120/14) A = 8.57 A

Thus the current in both the cases are different. This can be analysed by taking into account the resistance offered by the motor and resistor. Since in both the cases the resistances are different and hence the current are different in the circuits.

b) In the last question, let us try to find out the resistance offered by the motor when connected to the AC power supply. Since the power consumed by the motor when connected to a power source is given by

P = V²/R where V= voltage across the motor ; R= resistance offered by the motor

Then R= V²/P = (120²)/200 Ω = 72 Ω

Internal resistance of the circuit( r ) = 14 Ω

Then R_eff= R + r = 86 Ω

Now the current through the circuit is given by I = V / R_eff = (120) / 86 = 1.39 A

Thus the voltage drop across the motor in this case can be found by V = IR = (1.39 A) * (72 Ω) = 100.46 V

Voltage drop across the motor when the motor is connected without taking into account the internal resistance of the circuit is 120 V.

Hence the voltage drop across the motor in both the cases are different.