1. **Ohm's Law**: The relationship between voltage ($V$), current ($I$), and resistance ($R$) is given by $$V = IR$$. This means voltage equals current multiplied by resistance. 2. **Kirchhoff's Laws**: - Kirchhoff's Voltage Law (KVL): The sum of all voltages around any closed loop in a circuit is zero: $$\sum V = 0$$. - Kirchhoff's Current Law (KCL): The sum of currents entering a junction equals the sum leaving the junction: $$\sum I_{in} = \sum I_{out}$$. 3. **Power and Energy Relationships**: Electrical power ($P$) is the rate of energy consumption or production, given by $$P = VI = I^2R = \frac{V^2}{R}$$. Energy ($E$) used or produced over time $t$ is $$E = Pt$$. 4. **Series Circuits**: - Resistances add: $$R_{total} = R_1 + R_2 + \dots + R_n$$. - Current is the same through all components: $$I_{total} = I_1 = I_2 = \dots$$. - Voltage divides among resistors: $$V_{total} = V_1 + V_2 + \dots + V_n$$. 5. **Parallel Circuits**: - Reciprocals of resistances add: $$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$$. - Voltage is the same across all branches: $$V_{total} = V_1 = V_2 = \dots$$. - Currents add up: $$I_{total} = I_1 + I_2 + \dots + I_n$$. 6. **Combination Circuits** involve series and parallel groups combined, solved by reducing stepwise using above rules.