MHT CET · Physics · Electromagnetic Induction
Three inductances are connected as shown in figure. The equivalent inductance is
- A \(\frac{\mathrm{L}}{4}\)
- B \(\frac{5}{4} \mathrm{~L}\)
- C \(\frac{7}{4} \mathrm{~L}\)
- D L
Answer & Solution
Correct Answer
(D) L
Step-by-step Solution
Detailed explanation
Equivalent inductance of inductances connected in parallel is \(\mathrm{L}_{\mathrm{p}}=\frac{1}{\mathrm{~L}_1}+\frac{1}{\mathrm{~L}_2}\)
\(\therefore \quad \mathrm{L}_{\mathrm{p}}=\frac{1}{\left(\frac{2}{\mathrm{~L}}+\frac{2}{\mathrm{~L}}\right)}=\frac{\mathrm{L}}{4}\)
Equivalent inductance in series
\(\begin{aligned}
\mathrm{L}_{\mathrm{s}} & =\mathrm{L}_{\mathrm{p}}+\mathrm{L}_3 \\
& =\frac{\mathrm{L}}{4}+\frac{3}{4} \mathrm{~L}=\mathrm{L}
\end{aligned}\)
\(\therefore \quad \mathrm{L}_{\mathrm{p}}=\frac{1}{\left(\frac{2}{\mathrm{~L}}+\frac{2}{\mathrm{~L}}\right)}=\frac{\mathrm{L}}{4}\)
Equivalent inductance in series
\(\begin{aligned}
\mathrm{L}_{\mathrm{s}} & =\mathrm{L}_{\mathrm{p}}+\mathrm{L}_3 \\
& =\frac{\mathrm{L}}{4}+\frac{3}{4} \mathrm{~L}=\mathrm{L}
\end{aligned}\)
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