JEE Mains · Physics · STD 12 - 3. current electricity
In the circuit shown, the resistance \(r\) is a variable resistance. If for \(r = fR,\) the heat generation in \(r\) is maximum then the value of \(f\) is
- A \(\frac {1}{4}\)
- B \(1\)
- C \(\frac {1}{2}\)
- D \(\frac {3}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac {1}{2}\)
Step-by-step Solution
Detailed explanation
Heat generation in \(r\) will be, \(H=I_{r}^{2} r\) \(H=\left(\frac{V}{R+\frac{R r}{R+r}} \times \frac{r}{R+r}\right)^{2} r=\left(\frac{V}{R(R+2 r)}\right)^{2} r\) Putting \(\frac{d H}{d r}=0\) gives, \(r=\frac{R}{2} .\) Hence, \(f=\frac{1}{2}\)
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