Q. 213.9( 17 Votes )

Determine the current drawn from a 12V supply with internal resistance 0.5Ω by the infinite network shown in Fig. 3.32. Each resistor has 1Ω resistance.

Answer :

The resistance of each resistor connected in the given circuit, R = 1 Ω

Equivalent resistance of the given circuit = R’

The network is infinite. Hence, equivalent resistance is given by the relation,

R’ = 2 + (R’/R’ + 1)

or R’2 -2R’ -2 = 0

On solving R’ = (2+√4+8)/2

(Negative value of R’ cannot be accepted)

R’ = 1 + √3 Ω

R’ = 1 + 1.73 = 2.73 Ω

Internal resistance of the circuit, r = 0.5 Ω

Hence, total resistance of the given circuit = 2.73 + 0.5 = 3.23 Ω

Supply voltage, V = 12 V

According to Ω ’s Law, current drawn from the source is given by the ratio, = 12/3.23 = 3.72 A

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