# RL circuit equation

Avichal
Suppose a circuit with resistor R and inductor L with no source. I am trying to find kirchoffs equation for this circuit - I am getting iR -Ldi/dt = 0 as my equation which is apparently wrong. I just cannot understand how do I make equations for such circuits.

Homework Helper
Gold Member
Should that be iR + Ldi/dt = 0

Avichal
Yes it should be but I dont get it why. Voltage across resistor is iR and then voltage across inductor decreases by Ldi/dt so iR-Ldi/dt=0

$$\partial_t \vec{B}=-\vec{\nabla} \times \vec{E},$$
and integrate (line integral) along the circuit in direction of the positve current. Then the left-hand side translates into $L \frac{\mathrm{d} i}{\mathrm{d}t}$ for compact circuits, and the right-hand side you can transform into an integral along the surface, translating into $-R i$, where we have made use of Ohm's Law, $\vec{E}=\vec{j}/\sigma$. From this you get the desired equation,
$$L \frac{\mathrm{d} i}{\mathrm{d} t}=-R i.$$