Monday, June 10, 2019

electrical resistance - Sign of induced EMF and other elements in AC circuit


I am having problems to determine the direction of the induced EMF in AC circuits. For example, we have an inductor of inductance $L$. The induced EMF is given by:


$$ \epsilon = - L \frac{di}{dt} $$


where the minus sign is "explained" by the Lenz law. But how do I apply this to an AC current. The direction of current is changing (usually by sine or cosine laws). See the following link:


http://en.wikipedia.org/wiki/RLC_circuit#Series_RLC_circuit



for a series LCR circuit. Here the equation is given by


$$ L \frac{di}{dt} + Ri + \frac{1}{c}q = \epsilon_0 \sin (\omega t) $$


How do I know the sign of the first term on the left hand side... ? Why isn't it for example:


$$ - L \frac{di}{dt} + Ri + \frac{1}{c}q = \epsilon_0 \sin (\omega t) $$


When is it + and when -... Furthermore, how do I know the sign of any of the terms? The current is changing periodically. Why can't it be:


$$ L \frac{di}{dt} + Ri + \frac{1}{c}q = - \epsilon_0 \sin (\omega t) $$


My initial guess is that this depends on the point in time that we choose, but that ultimately gives us different solutions...




No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...