- a) R = 14 ohms, I = 0.70 b) 7.8 V
- 135 V
- 1.5 A
Explanation for Written:
1a: The 7 and 15 ohm resistors are like a single 22 ohm resistor. The 8 ohm, 12 ohm and “22 ohm” resistors in parallel make a 3.94 ohm resistor. Add this in series to the 10 ohm resistor and thats 13.94 ohms total. For total current, use ohms law with V = 9.7 volts and R = 13.94 ohms.
1b: find the voltage drop across the 10 ohm resistor – its 6.96 V (since you know the current there is 0.7 Amps.) Then find the current through the “22 ohm” resistor (you know the remaining voltage drop after the 10 ohm resistor (9.7 V – 6.96V). Use ohms law with that current for the voltage drop across the 7 ohm resistor. Add that voltage drop to the voltage across the 10 ohm resistor. Done.
2: Find V3.
V3 is also V2.
Total current is I2 + I3
I1 and I4 are both the same as total current.
Use ohms law to calculate V1 and V4.
Total voltage is V1 + V2 + V4
3: Total power output is 180 W (there are a total of 180 joules of energy leaving the circuit every second).
P = IV
180W = I(120V) – solve for I. Done.
Make a convoluted system of equations knowing that V2 = V3, I2 = I3, V1 + V2 = 120 V. I1 = I2 + I3, V1xI1 = 60W and so on. Solve these and substitute and you get the same answer.