Three resistors of 4.0 ohms, 6.0 ohms, and 12 ohms are connected in parallel to an applied potential difference of 12 volts. (1) Calculate the equivalent resistance. (2) Determine the potential difference across each resistor. (3) Calculate the current through each resistor.

(1) 2 ohms

(2) 12 Volts Across each resistor

(3) I₁ = 3 A, I₂ = 2 A, I₃ = 1 A

Explanation:

From the question,

(1) Equilvalent Resistance (Rt) for parallel connection is

1/Rt =(1/R₁)+ (1/R₂) + (1/R₃)

Where R₁ = 4 ohms, R₂ = 6 ohms, R₃ = 12 ohms

1/Rt = 1/4 +1/6 +1/12

1/Rt = (3+2+1)/12

1/Rt = 6/12

1/Rt = 1/2

Rt = 2 ohms.

(2) Since the resistors are connected in parallel, They will have the same potential difference across them,

Hence the P.d across each resistor = 12 Volts.

(3) For R₁,

I₁ = V/R₁ = 12/4

I₁ = 3 A.

For R₂,

I₂ = V/R₂

I₂ = 12/6

I₂ = 2 A

For R₃,

I₃ = V/R₃

I₃ = 12/12

I₃ = 1 A

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