A battery of 15 volt is connected to a parallel group of resistances of 4, 10…

For resistors connected in parallel across the same voltage source, the reciprocal of the equivalent resistance equals the sum of the reciprocals of each individual resistance: 1/Rp = 1/R1 + 1/R2 + 1/R3. The total current supplied by the source is then found from Ohm's law, I = V / Rp.

1. Write the parallel-combination formula for the three given resistances: 1/Rp = 1/4 + 1/10 + 1/20.

2. Express each term over the common denominator 20: 1/4 = 5/20, 1/10 = 2/20, and 1/20 = 1/20.

3. Add the terms: 1/Rp = (5 + 2 + 1)/20 = 8/20 = 2/5.

4. Invert the result to get the equivalent resistance: Rp = 20/8 = 2.5 ohm.

5. Apply Ohm's law with the 15 volt battery: I = V/Rp = 15/2.5 = 6 A.

As an independent check, find the current through each resistor separately under the same 15 volt supply: I1 = 15/4 = 3.75 A, I2 = 15/10 = 1.5 A, and I3 = 15/20 = 0.75 A. Since the three resistors share the same pair of nodes, the total current drawn from the battery is the sum of these branch currents: 3.75 + 1.5 + 0.75 = 6 A, which matches the equivalent-resistance method.

The current in the circuit is therefore 6 A.