# RL circuit equation

1. Sep 15, 2012

### 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.

2. Sep 15, 2012

### CWatters

Should that be iR + Ldi/dt = 0

3. Sep 16, 2012

### 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

4. Sep 16, 2012

### vanhees71

Draw your circuit and indicate an (arbitrary) direction, in which you want to count the current positive. Then use the right-hand rule to attach the surface-normal vector oriented positive relative to that direction of the current. Finally use Faraday's Law,
$$\partial_t \vec{B}=-\vec{\nabla} \times \vec{E},$$
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,
$$L \frac{\mathrm{d} i}{\mathrm{d} t}=-R i.$$

5. Sep 16, 2012

### Avichal

Sorry I am unaware of some of the things you said. Can you simplify please?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook