# Circuit with 2 sources of emf

by joshanders_84
Tags: circuit, sources
 P: n/a Treat the EMF sources and their resistances as separate components and apply the loop rule from any point on the circuit (I suggest using one of the EMF sources). Remember the current is constant throughout the system: $$16V - IR_1 - IR_2 - 8V - IR_3 - IR_4 = 0$$ I applied the law counterclockwise starting from EMF 1 but like I said you could start from anywhere. Solving for I you obtain the familiar $$I = \frac{\varepsilon_1 - \varepsilon_2}{R_1+R_2+R_3+R_4}$$ which looks a lot like $$I = \frac {\sum \varepsilon}{\sum R}$$ Hope this helps. Sorry but I don't know the LaTeX for that pretty little E my physics book uses so I figured lowercase epsilon suffices :)
 Emeritus Sci Advisor PF Gold P: 5,196 Circuit with 2 sources of emf Oh I see...the notation for the EMF's of the sources: try the \mathcal function--it gives you uppercase scripted characters, should you need them: $$\mathcal{E}$$ Sometimes for source voltages we just write $V_s$ instead. But since these are not ideal sources, it's good to distinguish between the EMF, which is defined as the potential difference between the two source terminals when no load is connected, vs. the actual voltage across the source when in this series circuit. If you already knew all of this...sorry to bore you to tears. I like these scripted letters...hmm...let's see...Laplace Transform: $$\mathcal{L} \{f(t)\}$$ it's cool...