Question

For the circuit shown in the diagram given below:



Calculate:
(a) the value of current through each resistor.
(b) the total current in the circuit.
(c) the total effective resistance of the circuit.

Answer 1

(a) All the resistors are connected in parallel. They are getting an equal voltage across their ends, which is equal to the voltage of the battery.

Hence, the current flowing through each resistor = $\frac{\mathrm{Voltage}\mathrm{across}\mathrm{the}\mathrm{battery}}{\mathrm{Resistance}\mathrm{of}\mathrm{the}\mathrm{resistor}}$

The voltage across the battery = 6 V

Current flowing through 5-ohm resistor = $\frac{6\mathrm{V}}{5\mathrm{\Omega }}=1.2\mathrm{A}$


Current flowing through 10-ohm resistor = $\frac{6\mathrm{V}}{10\mathrm{\Omega }}=0.6\mathrm{A}$

Current flowing through 30-ohm resistor = $\frac{6\mathrm{V}}{30\mathrm{\Omega }}=0.2\mathrm{A}$

(b) The total current in the circuit = Sum of the current through all the resistors = 1.2 A + 0.6 A + 0.2 A = 2 A

(c)The total resistance of the circuit$=\frac{\mathrm{Total}\mathrm{voltage}}{\mathrm{Total}\mathrm{current}}=\frac{6\mathrm{V}}{2\mathrm{A}}=3\mathrm{\Omega }$