Question
Inductors in series. Two inductors $L_{1}$ and $L_{2}$ are connected in series and are separated by a large distance so that the magnetic field of one cannot affect the other. (a) Show that the equivalent inductance is given by$$L_{\mathrm{eq}}=L_{1}+L_{2} .$$(Hint: Review the derivations for resistors in series and capacitors in series. Which is similar here?) (b) What is the generalization of (a) for $N$ inductors in series?
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Mathematically, this is given by $V = -L \frac{dI}{dt}$, where $L$ is the inductance, $I$ is the current, and $t$ is time. Show more…
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Inductors in series. Two inductors $L_{1}$ and $L_{2}$ are connected in series and are separated by a large distance so that the magnetic field of one cannot affect the other. (a) Show that the equivalent inductance is given by $$L_{\mathrm{eq}}=L_{1}+L_{2}$$ (Hint: Review the derivations for resistors in series and capacitors in series. Which is similar here? (b) What is the generalization of (a) for $N$ inductors in series?
Inductors in parallel. Two inductors $L_{1}$ and $L_{2}$ are connected in parallel and separated by a large distance so that the magnetic field of one cannot affect the other. (a) Show that the equivalent inductance is given by $$ \frac{1}{L_{\mathrm{eq}}}=\frac{1}{L_{1}}+\frac{1}{L_{2}} $$ (Hint: Review the derivations for resistors in parallel and capacitors in parallel. Which is similar here?) (b) What is the generalization of (a) for $N$ inductors in parallel?
Two inductors $L_{1}$ and $L_{2}$ are connected in series and are separated by a large distance. (a) Show that the equivalent inductance is given by $$ L_{\mathrm{eq}}=L_{1}+L_{2} $$ (Hint: Review the derivations for resistors in series and capacitors in series. Which is similar here?) (b) Why must their separation be large for this relationship to hold? (c) What is the generalization of (a) for $N$ inductors in series?
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