Unit 3 Electrical Circuits

Direction of Coventional Current

Direct of positive hole charge, opposite of electron flow.

Sides of battery and reminders when drawing

longer is positive side, shorter is negative, ALWAYS CONNECT IT DIRECTLY TO WIRE

Current

dq/dt. Is a VECTOR

EMF (ε)

Basically voltage (causes it)

NOT a force

Potential Difference of an open curcuit

STILL exists, just no current

ZERO charge flows

Finding amount of charge in a circuit

MUST take into the account the amounts of time

Circuit Symbols

Series Circuit Rules for V,I,R,C,Q

V: Sum

I: Equal

R: Sum

C: Inverses

Q: Equal

Parallel Circuit Rules for V,I,R,C,Q

V: Equal

I: Sum

R: Inverses

C: Sum

Q: Sum

Which circuit rules are opposite?

V and I/Q are opposite, C and R are opposite

What happens if there is a parallel branch with nothing on the branch? (circuit with 2+ branches)

Fuse blows

What happens to the Resistance of a wire if it is folded in half?

Length halves but AREA DOUBLES, so ¼ of Resistance

How to find total power and work

SCALAR sum

Resistivity

R = rho*L/A. As temperature increases, rho increases (for conductors). For insulators, it is inverse with temperature.

Ohmic means

Ideal

Direct Current

Current goes from the positive side of the battery (higher potential) to negative, supplied by a battery

Nonideal circuits parts

Have own internal resistance: voltmeter, ammeter, battery (tiny r)

For the battery, the voltage is V = emf - Ir

What happens to power if voltage is doubled?

Power is QUADRUPLED bc V²/R. Have to choose what is CONSTANT in the power formula to do 1:1:1 method

Resistance in parallel if all resistors have same value

R/# = Req

Equivalent Resistance

Series just add, parallel its the inverses - REMEMBER TO FLIP

How to check over circuits

Kirchoff’s Loop Rule: Total Voltage must be equal to 0 (count resistors as negative voltage)

Kirchoff’s Junction Rule: Sum of current going into a point must be same as sum going out

What happens to a nonideal battery over time?

Battery loses voltage and gains resistance

Current ALWAYS

Takes the path of least resistance

Power in Series vs parallel

Power increases with increasing resistance in series circuit (I²R) but decreases with increasing resistance in parallel (V²/R)

If a meter is NOT ideal, then…

it becomes a pathway in the circuit

Batteries use more power in

parallel than series because voltage is supplied to each branch he same in parallel (unless battery is put to maximum output)

What effect does adding branches in a parallel circuit have?

Voltage constant, power increases and total current increases while Req decreases

Why does resistance decrease in a parallel circuit?

Resistance decreases because there are multiple paths for the current to pass through

How to approach complex circuits

Split it into loops and do Kirchoff rules or break it into series and parallel (mashing sections of the circuit together to make it more simple and then working backwards towards the more complex circuit)

It’s like having multiple systems

Going from the positive end of a battery to the negative end indicates…

a voltage LOSS

Graphing voltage

must start and end at the same y value, going up if there is a battery or down with a resistor, flat for wire

Capacitors in a circuit

Take time to charge when attached to voltage source or discharge when not attached to source.

When charging, voltage increasing slowly over time until it levels off

Current decreases over time until it gets to 0

Capacitor takes ALL current from a circuit and acts as a short (even other parallel branches making them 0 A) until it is fully charged at which point it does not take any more current and the other pathways take all the current (slow exchange from capacitor to resistors)

Capacitor also changes I and P until it reaches steady state

Time Constant (τ)

τ = R_eqC_eq

The time constant is the amount of time it takes a capacitor to go from 0% to 63% of its total charge or steady state (or for discharging to go from 100% to 37%)

A larger τ means it takes more time to charge up (LESS steep slope)

Percentage derviived from V(t) = V₀(1-e^t/tau)

Rank the currents in this circuit

I_Z > ( I_W = I_X = I_Y )

W, X, and Y can all be connected to the battery without any resistors and then all converge and go downward, so Z has to have greater current equal to the magnitude of all 3 paths

Rank Currents

1 > 2 > 3=4

1 = 2+3, 3 and 4 are in series and have current equal to 2

How does a capacitor change as it charges?

Acts as a wire at first and then acts as an open switch where no current passes (0 resistance to infinite)