# Test Prep Splash

Hi everyone, just figured that I'd post an accumulation of what I've been studying for the test tomorrow morning. It goes in video order because that's the order that I learned the material in. If something is too vague, I reccomed looking at the video for elaboration

Circuits

- Current and Current Density
- Resistors and Resistance
- Circuits
- Voltmeters and Ammeters
- Ideal and Real Batteries
- RC Circuits: Steady State
- RC Circuits: Transient Analysis (Charging)

Current and Current Density:

Current measured in Amps, or charge per sec.

An electric field is applied to a conductor and a small field is created that opposes it

Avg. Velocity of electrons in that field= drift velocity (V_{d})

Vol= Bh = V_{d} * change in time * Area

# electrons = Volume * volume density(AKA "N")= N *change in time* V_{d} * Area

I= N*q*V_{d }*A

Current density = J* N*q*V_{d}

I= integral (J * dA)

J= I/A

Resistance ("Howdy, Y'all!" made my day in that vid, btw)

R=V/I

p = row =resistivity

R= pL/A

V= IpL/A

E=energy=V/L = p (I/A) = pJ

W=qV

I= dQ/dt

P=IV=I^{2}R=V^{2}/R

Circuits:

Series: Req= R1 +R2...

Parallel: 1/Req= 1/R1 +1/R2....

Kirchhoff's Current Law= sum all current entering = sum all current exiting (conserv. charge)

Kirchhoff's Voltage Law= sum of all potential drops in a closed loop of a circuit = 0 (conserv. energy)

Voltmeters and Ammeters:

Voltmeters: measures v between two points, high resistance, connected in parallel

Ammeters: measures current, low resistance, connected in series

Ideal and Real Batteries:

Ideal: no internal resistance

V battery = Emf = change in V

Real: has internal resistance

V battery = change in V = IR = Emf- (I)®, where r = internal resistance

For battery:

W= change in Q * Emf

P= W/change in time = (change in Q)(Emf)/(change in time)

P resistor (works for both external and internal) = I^{2}R

RC Steady State:

series: 1/Ceq= 1/C1 + 1/C2 ...

Parallel: Ceq = C1+C2...

RC Charging:

W= I^{2}R

U=1/2 C V^{2}

^{}

Time constant Tao=RC, occurs when quantity is 63% of its final value. 5 Tao= 99% final value (practically final value)

Note: an uncharged capacitor acts like a wire, a charged capacitor acts like a gap in the circuit (AKA no current)

...Okay, bed time. Good luck tomorrow, everyone!

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