Electric Circuits Cheat Sheet
The core ideas of Electric Circuits distilled into a single, scannable reference — perfect for review or quick lookup.
Quick Reference
Electric Current
The rate of flow of electric charge through a cross-section of a conductor: $I = \Delta Q / \Delta t$. Conventional current flows from high to low potential (positive terminal to negative terminal), while electrons actually drift in the opposite direction. The SI unit is the ampere (1 A = 1 C/s).
Voltage (Potential Difference)
The work done per unit charge in moving charge between two points in a circuit: $V = W/q$. A battery or power supply provides an electromotive force (EMF) that maintains a potential difference, driving current through the circuit. Measured in volts (1 V = 1 J/C).
Resistance and Ohm's Law
Resistance is the opposition to current flow in a conductor: $R = V/I$ (Ohm's law). It depends on the material's resistivity $\rho$, length $L$, and cross-sectional area $A$: $R = \rho L / A$. The SI unit is the ohm ($\Omega$). Ohmic materials have constant resistance; non-ohmic materials (like diodes) do not.
Series Circuits
Components connected end-to-end so the same current flows through each one. In a series connection, the total resistance is the sum: $R_{\text{total}} = R_1 + R_2 + \cdots$. The voltage divides among components proportionally to their resistances.
Parallel Circuits
Components connected across the same two nodes so each has the same voltage across it. The reciprocal of total resistance is the sum of reciprocals: $1/R_{\text{total}} = 1/R_1 + 1/R_2 + \cdots$. The total current divides among branches inversely proportional to their resistances.
Kirchhoff's Junction Rule
At any junction (node) in a circuit, the total current entering equals the total current leaving: $\sum I_{\text{in}} = \sum I_{\text{out}}$. This is a statement of conservation of electric charge -- charge does not accumulate at junctions in steady-state circuits.
Kirchhoff's Loop Rule
The sum of all voltage changes (gains and drops) around any closed loop in a circuit is zero: $\sum \Delta V = 0$. This is a statement of conservation of energy -- a charge that traverses a complete loop returns to its starting potential.
Capacitance
The ability of a device to store charge per unit voltage: $C = Q/V$. For a parallel-plate capacitor, $C = \epsilon_0 A / d$, where $A$ is plate area and $d$ is plate separation. Energy stored: $U = \frac{1}{2}CV^2$. The SI unit is the farad (F).
RC Circuits
Circuits containing both a resistor and a capacitor, exhibiting time-dependent (transient) behavior. The time constant $\tau = RC$ is the time for the voltage or current to change by a factor of $1 - 1/e \approx 63\%$. Charging: $V(t) = V_0(1 - e^{-t/RC})$. Discharging: $V(t) = V_0 e^{-t/RC}$.
Power in Circuits
The rate at which electrical energy is converted to other forms: $P = IV = I^2R = V^2/R$. In a resistor, electrical energy is dissipated as heat (Joule heating). The total power delivered by a battery equals the EMF times the current: $P = \varepsilon I$.
Key Terms at a Glance
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