stuff circuits blah

content/physics/CrazyStuff.md

@@ -104,5 +104,89 @@ $$
 
 Just as the potential energy of a raised ball does not depend on the gravitational field of the ball, the electric potential of the test charge $q$ doesn't depend on the magnitude of the charge itself. This quantity is given the unit **Volt**, or $1\text{ V}=1\;\text{J}/\mathrm{C}$ 
 
+# Circuits
+### Ohm’s Law:
+$$
+V = IR
+$$
+- Voltage $V$ = Current $I$ × Resistance $R$
+
+### Power in Circuits:
+$$
+P = IV
+$$
+- Power $P$ = Current $I$ × Voltage $V$
+
+$$
+P = I^2R
+$$
+- Power $P$ = Current squared $I^2$ × Resistance $R$
+
+$$
+P = \frac{V^2}{R}
+$$
+- Power $P$ = Voltage squared $V^2$ / Resistance $R$
+
+### Series Circuits:
+$$
+R_{\text{total}} = R_1 + R_2 + \dots + R_n
+$$
+- Total Resistance $R_{\text{total}}$ = Sum of Individual Resistances
+
+$$
+V_{\text{total}} = V_1 + V_2 + \dots + V_n
+$$
+- Total Voltage $V_{\text{total}}$ = Sum of Individual Voltages
+
+$$
+I_{\text{total}} = I_1 = I_2 = \dots = I_n
+$$
+- Current $I_{\text{total}}$ is the same across all components
+
+### Parallel Circuits:
+$$
+\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}
+$$
+- Total Resistance $R_{\text{total}}$ = Reciprocal Sum of Individual Resistances
+
+$$
+V_{\text{total}} = V_1 = V_2 = \dots = V_n
+$$
+- Voltage $V_{\text{total}}$ is the same across all components
+
+$$
+I_{\text{total}} = I_1 + I_2 + \dots + I_n
+$$
+- Total Current $I_{\text{total}}$ is the sum of individual currents
+
+### Capacitance:
+$$
+Q = CV
+$$
+- Charge $Q$ = Capacitance $C$ × Voltage $V$
+
+$$
+C = \frac{\epsilon_0 A}{d}
+$$
+- Capacitance $C$ of a parallel plate capacitor: $\epsilon_0$ = permittivity of free space, $A$ = area of plates, $d$ = distance between plates
+
+### Inductance:
+$$
+V = L \frac{di}{dt}
+$$
+- Voltage across an inductor $V$ = Inductance $L$ × Rate of change of current $\frac{di}{dt}$
+
+### RL Time Constant:
+$$
+\tau = \frac{L}{R}
+$$
+- Time constant $\tau$ for an RL circuit
+
+### Kirchhoff’s Laws:
+- **Kirchhoff’s Current Law (KCL):** The sum of currents entering a junction equals the sum of currents leaving.
+- **Kirchhoff’s Voltage Law (KVL):** The sum of voltages around any closed loop equals zero.
+
+
+
 ---
 #physics