SATHEE: Current Electricity 1 Question 7

Current Electricity 1 Question 7

7. A wire of resistance $R$ is bent to form a square $A B C D$ as shown in the figure. The effective resistance between $E$ and $C$ is $[E$ is mid-point of arm $C D]$

(2019 Main, 9 April I)

(a) $\frac{7}{64} R$

(b) $\frac{3}{4} R$

(d) $\frac{1}{16} R$

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Solution:

Let the length of each side of square $A B C D$ is $a$ .

$∴$ Resistance per unit length of each side $= \frac{R}{4 a}$

Now, $R_{1} = \frac{R}{4 a} [E C] = \frac{R}{4 a} \times \frac{a}{2} = \frac{R}{8}$

Similarly, $R_{2} = \frac{R}{4 a} [E D A B C] = \frac{R}{4 a} \times \frac{7 a}{2} = \frac{7 R}{8}$

Now, effective resistance between $E$ and $C$ is the equivalent resistance of $R_{1}$ and $R_{2}$ that are connected in parallel as shown below.

$\begin{aligned} R_{E C} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} & = \frac{(R / 8) \times (7 R / 8)}{(R / 8) + (7 R / 8)} \\ = \frac{7 R^{2}}{64} \times \frac{8}{8 R} = \frac{7}{64} R \end{aligned}$

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Current Electricity 1 Question 7

7. A wire of resistance $R$ is bent to form a square $A B C D$ as shown in the figure. The effective resistance between $E$ and $C$ is $[E$ is mid-point of arm $C D]$

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 1 Question 7

7. A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is [E is mid-point of arm CD]

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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7. A wire of resistance $R$ is bent to form a square $A B C D$ as shown in the figure. The effective resistance between $E$ and $C$ is $[E$ is mid-point of arm $C D]$