Question

Q152.Source IE irodov.

Figure shows that an infinite circuit is formed by repetition of the same link ,consisting of resistance R1=4 ohm and R2=3 ohm. find the resistance of this circuit between two points A and B.

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Answer 1

Answer:

Fig. 3.37 shows an infinite circuit formed by the repetition of the same link, consisting of resistance R1 = 4.0 Ω and R2 = 3.0 Ω. Find the resistance of this circuit between points A and

Answer 2

$Answer: 6ohm$

Given

• R1= 4ohm
• R2=3ohm

To Find

• Resistance between A and B

Concept

• If resistance are repeating upto infinite than we can assume same resistance between any repetation

Solution

let the Resistance between A and B is X than we can also assume Resistance of P and Q as X (because of inifinite combinations )

as R2 and X are In parallel total resistance of R2 and X is

$\frac{1}{R} = \frac{1}{R2} + \frac{1}{x} \rightrightarrows \: R = \frac{x \times \: R2 }{x +R2 }$

Now R1 and R in series than R equivalent=

$Req = R1 + R =R1 + \frac{R2 \times x}{R2 + x}$

But R equivalent is also X than

$x = R1+ \frac{R2 \times x}{R2+ x}$

From here

$x = \frac{R1 + \sqrt{ {R1}^{2} + 4R2R1} }{2}$

Putting values of R2 and R1

x=6ohms.

Additional information

• in infinitly repeating series resistance is capacitance at all repetation point is same