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please help me in solving out this problem.please reply me soon

please help me in solving out this problem.please reply me soon
 

Question Image
Grade:12th pass

1 Answers

Rajdeep
231 Points
2 years ago
HELLO THERE!
Here’s your answer:
 
Let,
R_{1} = R \\ \alpha_{1} = \alpha \\\\ R_{2} = 3R \\\alpha_{2} = 2\alpha
 
For parallel combination,
\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \\\\\\R_{eq} = \frac{R_{1}R_{2}}{R_{1} + R_{2}}
 
Again,
\frac{\alpha_{1}}{R_{1}} + \frac{\alpha_{2}}{R_{2}} = \frac{\alpha_{eq}}{R_{eq}} \\\\\\or, \alpha_{eq} = \frac{\alpha_{1}R_{2} + \alpha_{2}R_{1}}{R_{1} + R_{2}} \\\\= \frac{\alpha \times 3R + 2\alpha \times R}{4R} \\\\\\\alpha_{eq} = \frac{5}{4} \alpha
 
So, Option (A) is the correct answer!
 
THANKS!

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