Question

Example 11. Two 40 12 resistors and a 20 12 resistor are all connected in parallel with a 12 V power supply. Calculate their effective resistance and the current through each resistor. What is the current flowing through the supply? ​

Answer 1

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Answer 2

Correct Question

Two 40 Ω resistors and a 20 Ω resistor are all connected in parallel with a 12 V power supply. Calculate their effective resistance and the current through each resistor. What is the current flowing through the supply?

Answer

Given :

Three resistors are connected in parallel combination,

• R₁ = 40 Ω
• R₂ = 40 Ω
• R₃ = 20 Ω

Potential difference = 12 V

To find :

The effective resistance and the current through each resistor. What is the current flowing through the supply.

Solution :

we know that,

The reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. .i.e.,

1/R = 1/R₁ + 1/R₂

By substituting the values in the formula,

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

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{1}{40} + \dfrac{1}{40} + \dfrac{1}{20}$

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{1 + 1 + 2}{40}$

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{4}{40}$

$\dashrightarrow \sf \dfrac{1}{R_{eq}} = \dfrac{1}{10}$

$\dashrightarrow \sf R_{eq} = 10 \: ohms$

Thus, the effective resistance is 10 ohms.

Now, using ohms law let us find the current through each resistor.

Current accross R₁ :

➛ I₁ = V/R₁

➛ I₁ = 12/40

➛ I₁ = 0.3 A

Current accross R₂ :

➛ I₂ = V/R₂

➛ I₂ = 12/40

➛ I₂ = 0.3 A

Current accross R₃ :

➛ I₃ = V/R₃

➛ I₃ = 12/20

➛ I₃ = 0.6 A

The total current flowing through the supply is :

➛ I = I₁ + I₂ + I₃

➛ I = (0.3 + 0.3 + 0.6) A

➛ I = (0.6 + 0.6) A

➛ I = 1.2 A