JEE Mains · Physics · STD 12 - 3. current electricity
The charge flowing in a conductor changes with time as \(Q ( t )=\alpha t -\beta t ^2+\gamma t ^3\). Where \(\alpha, \beta\) and \(\gamma\) are constants. Minimum value of current is :
- A \(\alpha-\frac{3 \beta^2}{\gamma}\)
- B \(\alpha-\frac{\gamma^2}{3 \beta}\)
- C \(\beta-\frac{\alpha^2}{3 \gamma}\)
- D \(\alpha-\frac{\beta^2}{3 \gamma}\)
Answer & Solution
Correct Answer
(D) \(\alpha-\frac{\beta^2}{3 \gamma}\)
Step-by-step Solution
Detailed explanation
\(Q=\left(\alpha t-\beta t^2+\gamma t^3\right)\) \(i=\frac{d Q}{d t}=\left(\alpha-2 \beta t+3 \gamma t^2\right)\) \(\frac{d i}{d t}=(3 \gamma t-2 \beta)=0\) \(\Rightarrow t=\frac{\beta}{3 \gamma}\)…
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