Question

A microwave consists of two resistive components in series - the microwave generator thatconsumes 80v and a motor that turns the platter that has a resistance of 509. The microwaveplugs into the wall that gives a total of 120v. Draw the circuit and solve for Rt, Rgenerator, It,Vmotor.

Answer 1

Given data:

Voltage of the source;

`V_t=120\text{ V}`

Voltage across the generator;

`V_(generator)=80\text{ V}`

Resistance of the motor;

`R_(motor)=509\text{ }\Omega`

Circuit diagram:

In a series combination, the current flowing the circuit will be the same for all components, while the different potential differences across the different components.

The total potential of the circuit will be equal to the sum of the potential difference across different components. Therefore,

`V_t=V_(generator)+V_(motor)`

Here, V_motor is the potential difference across the motor.

The potential difference through the motor is given as,

`V_(motor)=V_t-V_(generator)`

Substituting all known values,

`\begin{gathered} V_(motor)=120\text{ V}-80\text{ V} \\ =40\text{ V} \end{gathered}`

Therefore, the voltage across the motor (V_motor) is 40 V.

According to the Ohm's law,

`V=IR`

Applying Ohm's law for the motor;

`V_(motor)=I_tR_(motor)`

Therefore, the current through the motor is given as,

`I_t=(V_(motor))/(R_(motor))`

Substituting all known values,

`\begin{gathered} I_t=\frac{40\text{ V}}{509\text{ }\Omega} \\ \approx0.0785\text{ A} \end{gathered}`

Therefore, the total current through the circut (I_t) is 0.0785 A.

Now applying Ohm's across the generator,

`V_(generator)=I_tR_(generator)`

The resistance of the generator is given as,

`R_(generator)=(V_(generator))/(I_t)`

Substituting all known values,

`\begin{gathered} R_(generator)=\frac{80\text{ V}}{0.0785\text{ A}} \\ \approx1019.11\text{ }\Omega \end{gathered}`

Therefore, the resistance of the generator (R_generator) is 1019.11 Ω.

In series combination, the total resistance of the circuit (R_t) is given as the sum of the resistance of individual components. Therefore,

`R_t=R_(generator)+R_(motor)`

Substituting all known values,

`\begin{gathered} R_t=1019.11\text{ }\Omega+509\text{ }\Omega \\ =1528.11\text{ }\Omega \end{gathered}`

Therefore, the total resistance (R_t) of the circuit is 1528.11 Ω.