JEE Mains · Physics · STD 12 - 3. current electricity
A current through a wire depends on time as \(i =\alpha_{0} t +\beta t ^{2}\) where \(\alpha_{0}=20 A / s\) and \(\beta=8 As ^{-2} .\) Find the charge crossed through a section of the wire in \(15 \,s\) (in \(C\))
- A \(2250\)
- B \(11250\)
- C \(2100\)
- D \(260\)
Answer & Solution
Correct Answer
(B) \(11250\)
Step-by-step Solution
Detailed explanation
\(i =20 t +8 t ^{2}\) \(i =\frac{ dq }{ dt } \Rightarrow \int d q =\int idt\) \(\Rightarrow q =\int_{0}^{15}\left(20 t +8 t ^{2}\right) dt\) \(q =\left(\frac{20 t ^{2}}{2}+\frac{8 t ^{3}}{3}\right)_{0}^{15}\) \(q =10 \times(15)^{2}+\frac{8(15)^{3}}{3}\) \(q =2250+9000\)…
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