Electricity Formula Sheet

Constants §

Coulomb’s Constant §

$$k=8.99\times 10^9\frac{{\text{ Nm}}^2}{{\text{C}}^2}$$

Electrostatic Forces §

Electric Force §

• $F_e$, electric force, in Newtons (N)
• $k$, Coulomb’s constant
• $q_1,q_2$, charge, in Coulombs (C)
• $r$, distance, in meters (m)
• $E$, electric field strength, in $\frac{N}{C}$

$$\begin{array}{rl}{F}_e& =\frac{k{q}_1{q}_2}{r^2}\\ & =qE\end{array}$$

Electric Field §

• $E$, electric field strength, in $\frac{N}{C}$
• $k$, Coulomb’s constant
• $q$, charge, in Coulombs (C)
• $r$, distance, in meters (m)

$$E=\frac{kq}{r^2}$$

Electric Energy §

Potential Energy §

• $PE$, potential energy, in Joules (J)
• $k$, Coulomb’s constant
• $q_1,q_2$, charge, in Coulombs (C)
• $r$, distance, in meters (m)
• $V$, voltage, in volts (V)

$$\begin{array}{rl}PE& =\frac{k{q}_1{q}_2}{r}\\ & =qV\end{array}$$

Voltage (Electric Potential) §

Voltage is essentially potential energy divided by charge— that’s why one of the $q$ charges cancels out.

• $V$, voltage, in volts, (V)
• $k$, Coulomb’s constant
• $q$, charge, in Coulombs (C)
• $r$, distance, in meters (m)
• $I$, current, in amps (A)
• $R$, resistance, in ohms ($\Omega$)

$$\begin{array}{rl}V& =\frac{kq}{r}\\ & =IR\end{array}$$

Change in Voltage §

• $\Delta V$, change in voltage, in volts (V)
• $\Delta PE$, change in potential energy, in joules (J)
• $q$, charge, in Coulombs (C)
• $E$, electric field strength, in $\frac{N}{C}$

$$\begin{array}{rl}\Delta V& =\frac{\Delta PE}{q}\\ & =Ed\end{array}$$

Work §

• $W$, work, in Joules (J)
• $q$, charge, in Coulombs (C)
• $E$, electric field strength, in $\frac{N}{C}$
• $d$, distance, in meters (m)
• $\Delta PE$, change in potential energy, in joules (J)
• $P$, power, in watts (W)
• $\Delta t$, change in time, in seconds

$$\begin{array}{rl}W& =-qEd\\ & =\Delta PE\\ & =P\Delta t\end{array}$$

Power §

• $P$, power, in watts (W)
• $I$, current, in amps (A)
• $R$, resistance, in ohms ($\Omega$)

$$\begin{array}{rl}P& =IV\\ & =\frac{V^2}{R}\end{array}$$

Circuits §

Capacitors §

See capacitors.

Capacitance §

• $C$, capacitance, in Farads (F)
• $Q$, charge, in Coulombs (C)
• $V$, voltage, in volts (V)

$$C=\frac{Q}{V}$$

Capacitor Potential Energy §

• $P{E}_C$, potential energy of capacitor, in Joules (J)
• $Q$, charge, in Coulombs (C)
• $V$, voltage, in volts (V)

$$P{E}_C=\frac{QV}{2}$$

Resistance §

Wire Resistance §

A wire’s resistance is directly proportional to its resistance and length, and inversely proportional to its cross sectional area— basically, width.

• $R$, resistance, in ohms ($\Omega$)
• $\rho$, resistivity, in ohm meters ($\Omega$m)
• $\ell$, length, in meters (m)
• $A$, cross-sectional area, in square meters (m${}^2$)

$$R=\rho \frac{\ell }{A}$$