Question

Three resistances of 5 Ω, 10 Ω and 30 Ω are connected in parallel
with a battery of 12 V. Find out
(a)the current passing through each resistance,
(b)the total current of the circuit,
(c) the equivalent resistance of the circuit.

Answer 1

Given :

Three resistances of 5 Ω, 10 Ω and 30 Ω are connected in parallel with a battery of 12 V.

1) We have to find equivalent resistance

Since , all three resistances are connected in parallel.

Thus,

$\blue{\dfrac{1}{R_{eq}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_2}+\dfrac{1}{R_3}}$

Now put the values then ,

Equivalent resistance 3 Ω.

2) We have to find the total current in the circuit.

E= 12 V

R = 3 Ω

Now , by ohms law

E= IR

I = 4 A

3) We have to find Current passing through each resistor .

Since , all three resistors are connected in parallel, so voltage across all three resistor same as battery voltage.

Current in 5 Ω resistor

V = I R

I = 12/5= 2.4 A

Current in 10 Ω resistor

V=I R

I = 12/10= 1.2 A

Current in 30 Ω resistor

V = I R

I = 12/30 = 0.4 A