- In this class, if a source inside red boxes is drawn, power & current are positive - For an element with a voltage drop $+V$ - Current flowing into positive (+) terminal -> power absorbed: $P=VI$ - Current flowing out of positive (-) terminal -> power delivered: $P=V(-I)=-VI$ - **Kirchhoff's Current Law**: currents entering at an essential node equal currents existing at that essential node - Essential node: location where 3+ circuit elements meet - **Kirchhoff's Voltage Law**: voltages in a closed loop path sum to zero: $\oint E\cdot d\ell=V(b)-V(a)=0$ - Always loop CW, preferably starting from lower left corner - **Voltage division** used to calculate the voltage drop across elements - Condition: elements *must* be in series w/ voltage source - $V_{x}=V_{s} \ast \frac{R_{x}}{R_{eq}}$ - $V_{s}$: source voltage - $V_{x}$: voltage across element of interest (E.O.I) - $R_{x}$: resistance of E.O.I - **Current division** used to calculate current across elements - Condition: elements *must* be in parallel - $I_{x}=I_{s} \cdot \frac{G_{x}}{G_{eq}}$ or $I_{x}=I_{s} \cdot \frac{R_{eq}}{R_{X}}$ - $I_{s}$: source element - $I_{x}$: current across E.O.I - $G_{x}$: conductance of E.O.I - $R_{x}$: resistance of E.O.I - In parallel, $G_{eq}=G_{1}+G_{2}+\dots$ or $\frac{1}{R_{eq}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\dots$ - $N$ identical parallel resistors: $R_{eq}=\frac{R}{N}$ - Two resistors in parallel: $R_{eq}=\frac{R_{1}R_{2}}{R_{1}+R_{2}}$ - In series, $\frac{1}{G_{eq}}=\frac{1}{G_{1}}+\frac{1}{G_{2}}+\dots$ or $R_{eq}=R_{1}+R_{2}+\dots$