Lecture 19

Readings

http://umdberg.pbworks.com/w/page/124451935/Workout%3A%20Kirchoff%27s%20principles

http://umdberg.pbworks.com/w/page/105378453/Example%3A%20Resistors%20in%20series

http://umdberg.pbworks.com/w/page/105379515/Example%3A%20Resistors%20in%20parallel

Nernst Review

Resistors in Series

T o t a l R e s i s t a n c e i n S e r i e s = \sum_{i = 1}^{n} (R_{i})

V o l t a g e D r o p o n I n d i v i d u a l R e s i s t o r = \frac{R e s i s t a n c e_{i n d i v i d u a l} Ω}{R e s i s t a n c e_{t o t a l} Ω} * (V o l t a g e_{t o t a l})

$R_{equivalent} = R_1 + R_2$

$\Delta V_{across\ R_1}$ :

Δ V_{a c r o s s R_{1}} = C u r r e n t (I) * R_{1} = \frac{V * R_{1}}{R e s i s t a n c e_{t o t a l / e q}} = \frac{V * R_{1}}{R_{1} + R_{2}}

Note regarding battery. I wrote it like:
- But really:
- $\Delta V = V_2 - V_1 = V$

Resistors in Parallel

T o t a l R e s i s t a n c e i n P a r a l l e l = R_{T} = \frac{1}{\sum_{i = 1}^{n} (\frac{1}{R_{i}})}

In series, current must go through 1 resistor, then the other
In parallel, it goes through one resistor or the other
Rule is "Reciprocals add"

\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \to a l g e b r a \to R_{e q} = \frac{R_{1} * R_{2}}{R_{1} + R_{2}}

I_{1} = \frac{V}{R_{1}}

I_{2} = \frac{V}{R_{2}}

Full voltage across each resistor (V)
$I_1$ $I_2$
$I = I_1 + I_2$

Clicker Questions