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Physics · 2023 · 2 marks
CBSE 2023 · Region 5 · Set 1 · Q25
Two coils C_1 and C_2 are placed close to each other. The magnetic flux φ_2 linked with the coil C_2 varies with the current I_1 flowing in coil C_1,…
Two coils $\displaystyle \mathrm{C}_{1}$ and $\displaystyle \mathrm{C}_{2}$ are placed close to each other. The magnetic flux $\displaystyle \phi_{2}$ linked with the coil $\displaystyle \mathrm{C}_{2}$ varies with the current $\displaystyle \mathrm{I}_{1}$ flowing in coil $\displaystyle \mathrm{C}_{1}$, as shown in the figure. Find
(A)(i)
the mutual inductance of the arrangement, and
(ii)
the rate of change of current $\displaystyle \left(\frac{\mathrm{dI}_{1}}{\mathrm{dt}}\right)$ that will induce an emf of $\displaystyle 100$ V in coil $\displaystyle \mathrm{C}_{2}$.
Marking-scheme solution
(i) \(\displaystyle \phi_{2}=\mathrm{M} \mathrm{I}_{1}\) Slope of the graph, \(\displaystyle \mathrm{M}=\frac{\phi_{2}}{\mathrm{I}_{1}}\)
\[\mathrm{M}=2.5 \mathrm{H}
\]
(ii) \(\displaystyle \left|\varepsilon_{2}\right|=\mathrm{M} \frac{d \mathrm{I}_{1}}{d t}\)
\[\frac{d \mathrm{I}_{1}}{d t}=\frac{\left|\epsilon_{2}\right|}{\mathrm{M}}=\frac{100}{2.5}=40 \mathrm{As}^{-1}
\]
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