Physics

Observe the given circuit diagram and answer the questions that follow :
(a) Calculate the resistance of the circuit when the key K completes the circuit.
(b) Calculate the current through 3 Ω resistance when the circuit is complete.

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(a) 5Ω and 3Ω are in series so their equivalent resistance (R_s) = 5 + 3 = 8Ω

Now 2Ω and R_s are in parallel.

$\dfrac{1}{\text R$

From circuit diagram,

Internal Resistance = 0.4 Ω

Total resistance of circuit = 1.6 + 0.4 = 2 Ω

(b) Current drawn from the battery :

$\text I = \dfrac{\text {emf}}{\text {Total resistance}} \\[1em] ⇒ \text I = \dfrac{4}{2} = 2\ \text A$

Now, the current I divides in 2 parts.

Let current across 2Ω be I₁ and across the series combination of 5Ω and 3Ω be I₂.

I = I₁ + I₂ = 2 A …………..(1)

Terminal Voltage of cell = V = IR_p = 2 x 1.6 = 3.2 V

∴ P.d. across 2 Ω resistor = 3.2 V

I₁ = $\dfrac{3.2}{2}$ = 1.6 A

Substituting value of I₁ in Eq 1,

2 = 1.6 + I₂

⇒ I₂ = 2 - 1.6 = 0.4 A

Hence, current across 3Ω = 0.4 A

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