SATHEE: Current Electricity 2 Question 27

Current Electricity 2 Question 27

27. An infinite ladder network of resistances is constructed with $1 Ω$ and $2 Ω$ resistances, as shown in figure.

The $6 V$ battery between $A$ and $B$ has negligible internal resistance.

(1987, 7M)

(a) Show that the effective resistance between $A$ and $B$ is $2 Ω$ .

(b) What is the current that passes through the $2 Ω$ resistance nearest to the battery?

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Solution:

(a) Let $R_{A B} = x$ . Then, we can break one chain and connect a resistance of magnitude $x$ in place of it.

Thus, the circuit remains as shown in figure.

Now, $2 x$ and $x$ are in parallel. So, their combined resistance is $\frac{2 x}{2 + x}$

$or R_{A B} = 1 + \frac{2 x}{2 + x}$

But $R_{A B}$ is assumed as $x$ . Therefore,

$x = 1 + \frac{2 x}{2 + x}$

Solving this equation, we get

$x = 2 Ω$

Hence proved.

(b) Net resistance of circuit $R = 1 + \frac{2 \times 2}{2 + 2} = 2 Ω$

$∴$ Current through battery $i = \frac{6}{2} = 3 A$

This current is equally distributed in $2 Ω$ and $2 Ω$ resistances. Therefore, the desired current is $\frac{i}{2}$ or $1.5 A$ .

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Current Electricity 2 Question 27

27. An infinite ladder network of resistances is constructed with $1 Ω$ and $2 Ω$ resistances, as shown in figure.

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Current Electricity 2 Question 27

27. An infinite ladder network of resistances is constructed with 1Ω and 2Ω resistances, as shown in figure.

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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27. An infinite ladder network of resistances is constructed with $1 Ω$ and $2 Ω$ resistances, as shown in figure.