If E1 = 120 volts, E2 = 240 volts, and R2 = 80 ohms, what is R1 in the series circuit?

In a series circuit, the total voltage is the sum of the voltages across each resistor, and the total current flowing through the circuit is the same for all components. According to Kirchhoff's voltage law, the sum of the voltages in any closed loop is equal to the total voltage supplied.

Given that E1 = 120 volts and E2 = 240 volts, you can find the total voltage in the circuit. The total voltage is the sum of E1 and E2:

Total Voltage = E1 + E2 = 120 volts + 240 volts = 360 volts.

Now, using Ohm's law (V = I × R), the total resistance in the series circuit can also be expressed using the total voltage and the total current:

R_total = (E1 + E2) / I.

The currents through both resistors can be expressed as:

I = E1 / R1 = E2 / R2.

This gives us two equations based on voltage drops across R1 and R2:

R1 = E1 / I and R2 = E2 / I.

Now, if we can express I in terms of R2 and E2, we can substitute it back into our equation for R