# Induced Emf in an Inductor in an LRC circuit

**1. The problem statement, all variables and given/known data**

In the circuit shown in the figure, the switch S is closed at time t=0 with no initial charge on the capacitor. What is the induced emf if the inductor at time t=0?

**2. Relevant equations**

ε=-LdI/dt

**3. The attempt at a solution**

Initially the inductor acts like a broken wire in that no current can go through it so the potential difference across the 100 Ω resistor is 0. The capacitor initially has 0 resistance, so all the current will flow through there and the voltage across the 50Ω resistor in parallel with the capacitor (V4) will also be zero. So a time t=0 it acts like a simple circuit with resistance 50 Ω and εbattery 40 V. I am unsure if there would also be a potential difference across the inductor due to an induced emf. I don’t really know how to find the current as a function of time for this combination circuit so I’m not sure if dI/dt would then be zero, making the induced emf zero. Any help is appreciated!

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