MHT CET · Physics · Electromagnetic Induction
An inductor coil of inductance \(L\) is divided into two parts and both parts are connected in parallel. The net inductance is
- A L
- B 2 L
- C \(\frac{\mathrm{L}}{2}\)
- D \(\frac{\mathrm{L}}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{L}}{4}\)
Step-by-step Solution
Detailed explanation
Inductance is proportional to the length of the coil so each part will have inductance \(\frac{\mathrm{L}}{2}\)
Net inductance \(=\frac{\mathrm{L}_1 \mathrm{~L}_2}{\mathrm{~L}_1+\mathrm{L}_2}=\frac{\frac{\mathrm{L}}{2} \times \frac{\mathrm{L}}{2}}{\frac{\mathrm{~L}}{2}+\frac{\mathrm{L}}{2}}=\frac{\mathrm{L}}{4}\)
Net inductance \(=\frac{\mathrm{L}_1 \mathrm{~L}_2}{\mathrm{~L}_1+\mathrm{L}_2}=\frac{\frac{\mathrm{L}}{2} \times \frac{\mathrm{L}}{2}}{\frac{\mathrm{~L}}{2}+\frac{\mathrm{L}}{2}}=\frac{\mathrm{L}}{4}\)
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