Since the current is 2 amp, we need to determine the fraction of the current flows through the 30 Ω resistor and the fraction of the current flows through the rest of circuit. As I look at the rest of the circuit, I see two 20 Ω resistors that are in parallel and a 40 Ω resistor that is in series with them. To determine the equivalent resistance, I use the following process.
For the two 20 Ω resistors, R eq= 10 Ω
For the entire branch, Req= 10 + 40 = 50 Ω
Now we have 30 Ω resistor that is in parallel with a 50 Ω. Since these two resistors are in parallel, we can use the following equation to determine their equivalent resistance.
1/Req = 1/30 + 1/50 = 18.75 Ω
Now I know where you got this number. We can use this number and the 2 amps in the following equation to determine the voltage of the battery.
V = I * R = 2 * 18.75 = 37.5 volts
Now we need to look at the circuit that has the 30 and 50 in parallel. In a parallel circuit, the voltage is the same for both resistors. To determine the current, use the same equation.
37.5 = I * 30, I = 37.5/30 = 1.25
37.5 = I * 50, I = 37.5/50 = 0.75 amp
The 0.75 amp flows through the 40Ω resistor.
V = 40 * 0.75 = 30 volts
To determine the voltage of the two 20 Ω resistors, subtract this number from the battery voltage.
V = 37.5 = 30 = 7.5
To determine the current through each of these resistors, use the same equation.
7.5 = I * 20, I = 7.5/20 = 0.375 amps
The 2 x 20's in parallel = 10 ohms equivalency. In series with 40 ohms, = 50 ohms.
The 50 ohms is in parallel with the 30 ohms, so equivalency = (50 x 30)/(50 + 30) = 18.75 ohms total.
With 2A. flowing in the circuit, the applied voltage is (IR) = 2 x 18.75 = 37.5 volts.
R3 in parallel with R4 = 10 ohms
(Hint: Rx in parallel with Rx gives Rx/2)
Add R2 in series... 10 + 40 = 50 ohms
In parallel with R1...
1/R = 1/30 + 1/50 = (1/150)*(5 + 3) = 8/150
R across "v" = 150/8 ohms.
I can understand your confusion because "v" is marked with a *current*, and "v" is a symbol usually reserved for voltage.
Anyway, if the (badly-named) "v" supplies 2 amps, the voltage across it is current*resistance
= 2*150/8 volts
=150/4 volts.
1/R' = 1/20 + 1/ 20
R' = 10
R" = 40 + 10 = 50
1/ Rt = 1 / 30 + 1 / 50
Rt = 18.75
E = 2A * 18.75 = 37.5V
Finding this particular circuit difficult as both R3 and R4 are the same. The answer I got was 18.75 ohms. Also I have to calculate the supply voltage but I am unsure if that would just be 2 Amps or not because we usually work in volts so I have got a feeling its not that simple.
thanks
