X and Y are two circuits having coefficient of mutual inductance 3 mH and resistances $10 \Omega$ and $4…

X and Y are two circuits having coefficient of mutual inductance 3 mH and resistances $10 \Omega$ and $4 \Omega$ respectively. To have induced current $60 \times 10^{-4} \mathrm{~A}$ in circuit Y , the amount of current to be changed in circuit X in 0.02 sec is
  1. 1.6 A
  2. 0.16 A
  3. 0.32 A
  4. 3.2 A

Solution

$\begin{aligned} & \text { } \mathrm{M}=3 \mathrm{mH}=3 \times 10^{-3} \mathrm{H}, \mathrm{R}_1=10 \Omega, \mathrm{R}_2=4 \Omega \text {, } \\ & \mathrm{I}_2=60 \times 10^{-4} \mathrm{~A}, \Delta \mathrm{t}=0.02 \end{aligned}$ $\therefore \quad$ Induced current in Y is $\begin{aligned} & \mathrm{I}_g=\frac{e_2}{\mathrm{R}_2}=\left(\frac{\mathrm{M} \cdot \Delta \cdot \mathrm{I}}{\Delta t}\right) \frac{1}{\mathrm{R}_2} \\ & \Rightarrow \Delta \mathrm{I}_1=\frac{\mathrm{I}_2 \times \Delta \mathrm{t} \times \mathrm{R}_2}{\mathrm{M}}=\frac{60 \times 10^{-4} \times 0.02 \times 4}{3 \times 10^{-3}}=0.16 \mathrm{~A} . \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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