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  • 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.

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.

    

Answers (1)

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First, let us find the equivalent of the infinite network,

Let the Equivalent resistance of the given circuit = R.

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

R'=2+\frac{R'}{R'+1}

R'^2- 2R'-2=0

R'=\frac{2 \pm \sqrt{12}}{2}=1\pm \sqrt{3}

A negative value of R’ cannot be accepted. Hence, equivalent resistance,

R'=1+ \sqrt{3} =1+1.73=2.73\Omega

The internal resistance of the circuit, r = 0.5 Ω and the supply voltage, V = 12 V ,

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

Hence, According to Ohm’s Law, the current drawn from the source is given by the ratio

 =\frac{12}{3.23}=3.72 \ Amp

Posted by

Pankaj Sanodiya

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