Question

Three resistors of resistances 5ohm, 10ohms and 20ohms are connected parallel to a battery
of 12V. Calculate;
a) The current through each resistor.

b) The total current in the circuit.

c) Total resistance in the circuit.​

Answer 1

Answer:

Explanation:

Given :

• R¹ = 5 Ω , R² = 10 Ω , R³ = 20 Ω are connected in parallel combination.
• Volt (v) = 12 V

To Find :

• I) The current through each resistor.
• II) The total current in the circuit.
• III) Total resistance in the circuit.

Formula to be used :

• Ohms law formula, .ie,, V = IR
• Total current formula, ie,, I = I¹ + I² + l³

If resistance is connected in parallel, the parallel resistance is given by :-

• 1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4,...1/Rn

Solution :

★Case(I), The current through each resistor.

I¹ = V/R¹

⇒I¹ = 12/5

⇒I¹ = 2.4 A★

I² = V/R²

⇒ I² = 12/10

⇒ I² = 1.2 A★

I³ = V/R³

⇒ I³ = 12/20

⇒ I³ = 0.6 A★

★Case(II), The total current in the circuit.

I = I¹ + l² + l³

⇒ I = 2.4 + 1.2 + 0.6

⇒ I = 3.6 + 0.6

⇒ I = 4.2 A★

★Case(III), Total resistance in the circuit.

1/Rp = 1/R1 + 1/R2 + 1/R3

⇒ 1/Rp = 1/5 + 1/10 + 1/20

⇒ 1/Rp = 5 + 10 + 20/5 × 10 × 20

⇒ 1/Rp = 35/1000

⇒ 1/Rp = 0.035 Ω★