AP Physics C: E&M Unit 11 Formulas

Drift-velocity equation for current?

I=(ne)v_eA

Derivative formula for current?

I=\frac{Q}{\Delta t}=\frac{dq}{dt}

Current density equation?

J=\frac{I}{A}

Dot-product formula for current?

I=\vec{J}\cdot \vec{A}=|J||A|cos(\theta)

Integral form for current?

I=\int \vec{J}\cdot d\vec{A}

E-field and current density equation?

\vec{E} =\rho \vec{J}

Formula for resistivity/conductivity?

\rho =\frac{1}{\sigma}\Rightarrow \sigma =\frac{1}{\rho}

Resistivity/resistance equation?

R=\rho \frac{L}{A}

Formula for power?

P=IV=I²R=\frac{V²}{R}

Voltage formula?

\Delta V=IR

What is Kirchhoff’s Junction rule?

States that the currents leaving and entering a junction are equal to each other

I_1+I_2+I_3+…+I_n=I_{tot}

What is Kirchhoff’s Loop Rule?

States that in a closed loop of circuit, the sum of all voltage drops is zero (based on the law of conservation of charge)

\Delta U_E=q\Delta V

Formula for voltage of a charging capacitor in an RC circuit?

V_c(t)=V_b(1-e^{-\frac{t}{RC}}) q

Formula for the charge on a charging capacitor in an RC circuit?

Q(t)=CV_b(1-e^{-\frac{t}{RC}})

Formula for voltage of a charging resistor in an RC circuit?

V_R(t)V_be^{-\frac{t}{RC}}

Formula for current of a charging resistor in an RC circuit?

I(t)=\frac{V_b}{R}e^{-\frac{t}{RC}}

Formula for voltage of a discharging capacitor in an RC circuit?

V_c(t)=V_be^{-\frac{t}{RC}}

Formula for charge of a discharging capacitor in an RC circuit?

Q(t)=Q_0e^{-\frac{t}{RC}}

Formula for voltage of a discharging resistor in an RC circuit?

V_R(t)=V_be^{-\frac{t}{RC}}

Formula for current of a discharging resistor in an RC circuit?

I(t)=-\frac{V_b}{R}e^{-\frac{t}{RC}}

What does voltage of a charging capacitor reach after a long time?

V_c=V_b

What does charge of a charging capacitor reach after a long time?

Q=CV_b

What does voltage of a charging resistor reach after a long time?

V_R=0

What does current of a charging resistor reach after a long time?

I=0

Voltage/charge for a fully-discharged capacitor?

V_c=Q=0

Voltage/current through a resistor on an empty capacitor?

V_R=I=0

Time constant formula?

\tau = R_{eq}C_{eq}