Question

two resistor of resistance of 10 ohms and 20 ohms are connected in parallel. A battery supplies a current of 6A to the combination. Calculate the current in each of the resistor and power of each resistor​

Answer 1

Answer :-

→ Current in 10 Ω resistor = 4 A

→ Current in 20 Ω resistor = 2 A

→ Power of the 10 Ω resistor = 160 W

→ Power of the 20 Ω resistor = 80 W

Explanation :-

We have :-

→ 1st resistance (R₁) = 10 Ω

→ 2nd resistance (R₂) = 20 Ω

→ Total current (I) = 6 A

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The current in the 10 Ω resistor is :-

I₁ = (R₂/R₁ + R₂) × I

⇒ I₁ = (20/10 + 20) × 6

⇒ I₁ = 20/30 × 6

⇒ I₁ = 4 A

The current in the 20 Ω resistor :-

I₂ = (R₁/R₁ + R₂) × I

⇒ I₂ = (10/10 + 20) × 6

⇒ I₂ = 10/30 × 6

⇒ I₂ = 2 A

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Power of 10 Ω resistor :-

P₁ = I²₁ × R₁

⇒ P₁ = (4)² × 10

⇒ P₁ = 16 × 10

⇒ P₁ = 160 W

Power of 20 Ω resistor :-

P₂ = I²₂ × R₂

⇒ P₂ = (2)² × 20

⇒ P₂ = 4 × 20

⇒ P₂ = 80 W

Answer 2

Given :-

Two resistor of resistance of 10 ohms and 20 ohms are connected in parallel. A battery supplies a current of 6A to the combination

To Find :-

Current in each of the resistor and power of each resistor​

Solution :-

We know that

For 1st resistor

Current = Current(Battery) × (Resistance 2/Sum of resistors)

Current = 6 × (20/10 + 20)

Current = 6 × 20/30

Current = 120/30

Current = 4 A

For 2 nd resistor

Current = Current(Battery) × (Resistance 1/Sum of resistors)

Current = 6 × (10/20 + 10)

Current = 6 × (10/30)

Current = 60/30

Current = 2 A

For Power

1]

P = RI²

P = 10 × (4)²

P = 10 × 16

P = 160 watt

2]

P = RI²

P = 20 × (2)²

P = 20 × 4

P = 80 watt