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schematic

simulate this circuit – Schematic created using CircuitLab

The circuit above has total power dissipation of 60 watts. I need to calculate:

- Resistance of R2

Since it is given that total power is 60 watts, and the series circuit has 120v, then we can calculate total resistance to be RT = (120*120)/60 = 240 ohms

We know we currently have a total known resistance of R1 + R3 = 180 ohms. So R2 = 240 - 180 = 60 Ohms

- Current in the circuit

If we calculated resistance of R2 correctly, then we know RT = R1+R2+R3 = 240 ohms

We know voltage gain VT = 120 Volts.

So total current: IT = VT/RT = 120/240 = 0.5 Amps

- Voltage across each resistor

Voltage across R1 = V1 = (0.5 A) * (80 ohms) = 40 Volts

Voltage across R2 = V1 = (0.5 A) * (60 ohms) = 30 Volts

Voltage across R3 = V1 = (0.5 A) * (100 ohms) = 50 Volts

To check if our answer is correct we total the voltages 40+30+50 = 120 Volts which is our total voltage.

Are my answers correct?

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Your answers look correct.

As a cross check, you are given the voltage (120V) and the total power (60W). From that you can calculate the current directly.

P=EI, so 60W=120V*I.
I therefore has to be .5A, which matches your other results.

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