Ohm's Law, problems:

Determine the total resistance and potential difference between points a and b in the circuit shown. Also determine the current in, and the potential difference across, each resistor. The input current is 60 A.

• Total resistance between a and b. First, calculate the 12, 6, and 4 ohm parallel combination R//1

  1/R//1 = 1/12 + 1/6 + 1/4 = 1/2. Then R//1 = 2 ohm.

  The upper branch is 3 ohms in series with R//1, 3 ohm + 2 ohm = 5 ohm. This 5 ohm resistor is in parallel with the 20 ohm resistor, equivalent to a single resistor R//2 = 5 ohm//20 ohm:

  1/R//2 = 1/5 + 1/20 = 1/4. Then R//2 = 4.

  The total resistance between a and b is 4 ohm + 5 ohm = 9 ohms. The voltage drop or potential difference between points a and b is 60Ax9ohm = 540 V.
• To obtain the individual currents and voltages in each resistor we can proceed as follows (there is no a unique method): The voltage across R//2 is the difference between the total 540 voltage and the voltage drop in the 5 ohm resistor. This drop is 60A*5ohm = 300 V. So the potential difference across R//2 is 540 V - 300 V = 240 V.

Now we can calculate the currents and voltages in the R//2combination:

In the 20 ohm resistor: current= 240 V/20 ohm = 12 A, voltage = 240 V The upper branch has then a current of 60 A - 12 A = 48 A, or alternatively 240 V/5 ohm = 48A.

The 3 ohm resistor has a voltage of 48 Ax3 ohm = 144 V.

The R//1 combination presents a voltage of 48 AxR//1 = 48 Ax2 ohm = 96 V, or alternatively 240 V - 144 V = 96 V. The currents in the 12 ohm, 6 ohm and 4 ohm are respectively 96/12 A=8 A, 96/6=16 A and 96/4=24 A.