When calculating things about a circuit, a useful and efficient process to do (for simple circuits) is called the RIVIP process. It stands for:
- R: Calculate the total Equivalent Resistance
- I: Calculate the total current
- VI: Calculate the voltages to different branches
- P: Calculate power
So, the first step is to calculate the equivalent resistance. There are two formulas for equivalent resistance: parallel and series.
For series circuits, or the most simple kind of circuits, the equivalent resistance is simply the sum of the resistances.
For parallel circuits (right part of the circuit above), the resistance is the reciprocal of the sum of the reciprocals of the resistances. (shown below)
Parallel: 1/req = 1/r1 + 1/r2 + 1/r3 + ... + 1/rN Series: req = r1 + r2 + r3 + ... + rN
So, now we must plug that formula in. For the series part, you sum them together.
Req = 11 + 4 = 15 1/Req = 1/2 + 1 = 3/2 Req = 2/3
By summing them together, you now know the equivalent resistance is 15 + 2/3, or 47/3.
V = IR, and V = 17 volts, so 17 = I(47/3).
V = 17, R = 47/3 V = IR 51/3 = I(47/3) 51/47 = I Current = 51/47 Amperes
Now, we go through and check:
V = IR First: V = (51/47)(4) = 4.34V Last: V = (51/47)(11) = 11.94 V Parallel: First: 1(2/3)(51/47) = .72 V Second: 2(1/3)(51/47) = .72 V 4.34 + 11.94 + .72 = 17
The reason I multiplied 2/3 and 1/3 in the parallel circuit is because since the resistance is smaller on the right side of the parallel circuit, more current can flow. Precisely 2/3 of the current flows there, since the resistance is two times less than the other side. Now, we verified the the voltage is the same on both sides of a parallel circuit, ad the total voltage was in fact 17 volts.
Finally, we calculate power. Power = current * voltage, which equals 18.446 Watts.