Circuits, resistors, capacitors test physics C

When finding the current in branches of a multiloop circuit

Choose arbitrary directions for i. If at the very end, you get a negative value for i, that means the direction you chose was wrong - reverse it at the very end.

Junction rule

The sum of currents entering a junction must be equal to the sum of currents leaving that junction

Resistances in parallel

Resistors in parallel have the same potential difference V - par-v

Equivalent resistance in parallel

1/R equivalent = 1/R1 + 1/R2 + 1/R3 + …

Resistances in series

Resistors connected in series have the same current i across each - ser-i

Equivalent resistance in series

R equivalent = R1 + R2 + R3 + …

Finding potential difference between any two points in a circuit

Start at one point and traverse the circuit to the other point along any path, and add algebraically the changes in potential you encounter

Resistance rule

Change in potential across a resistor going the direction of the current = -iR

EMF rule

Change in potential across a battery going the direction of the current = (E)

Power of an EMF device

P = i(E)

Power

P = iV, P = i² R, P = V² /R, lightbulb gets brighter with more power through it

EMF (E)

(E) = dw (work) / dq (charge)

Units for a volt

Joule / coulomb

Current through a simple circuit

i = V/R

Resistance through a wire

R = (p) L/A, (p) is resistivity, L is length, A is area of cross-section

Units of an amp

Coulomb / second

Voltage potential difference between plates of a capacitor

Vc = q/c

Current when charging a capacitor

Current is zero when the plates have same potential difference as terminals of the battery

Equilibrium/final charge on a capacitor

q = C(E)

Charging equation for a capacitor

R * dq/dt + q/C = (E)

Charge on the plates of a capacitor being charged

q = C(E)(1 - e^-t/RC )

Current while charging a capacitor

i = dq/dt = ((E)/R) * e^-t/RC

How a capacitor behaves while being charged

Initially, capacitor acts like an ordinary connecting wire relative to the charging current. A long time later, it acts like a broken wire.

Voltage potential difference while charging a capacitor

Vc = q/C = (E)(1 - e^-t/RC )

Capacitative time constant

Tau = RC

Discharging equation

R * dq/dt + q/C = 0

Charge when discharging a capacitor

q = q₀ * e^-t/RC

Current when discharging a capacitor

i = dq/dt = -(q₀ / RC) * e^-t/RC

Potential energy of capacitor

E = q² / 2C = CV² / 2