Circuit Theory (Electrical)

Basic Laws:

• Ohm's law: V = IR.
• Power: P = VI = I²R = V²/R.

Kirchhoff's Laws:

• KCL: sum of currents at a node = 0.
• KVL: sum of voltages around a loop = 0.

Resistors:

• Series: R_total = R1 + R2 + ...
• Parallel: 1/R_total = 1/R1 + 1/R2 + ...
• Color code: 4-band & 5-band.

Capacitors:

• C = Q/V. Unit: farad (F).
• Series: 1/C = 1/C1 + 1/C2.
• Parallel: C_total = C1 + C2.
• Energy = ½CV².

Inductors:

• V = L·di/dt. Unit: henry (H).
• Series: L_total = L1 + L2.
• Parallel: 1/L = 1/L1 + 1/L2.
• Energy = ½LI².

Network theorems:

• Thevenin's: any network → equivalent V_Th + R_Th.
• Norton's: any network → I_N + R_N.
• Superposition: linear circuits — analyze each source separately.
• Maximum Power Transfer: R_load = R_source.

AC Circuits:

• v(t) = V_max sin(ωt + φ).
• RMS = V_max/√2.
• Reactance: X_L = ωL; X_C = 1/(ωC).
• Impedance: Z = √(R² + (X_L − X_C)²).
• Power factor: cos φ.
• Resonance: X_L = X_C; f_r = 1/(2π√(LC)).

Three-phase:

• Line voltage = √3 × phase voltage (star).
• Line current = √3 × phase current (delta).
• Power: P = √3 × V_L × I_L × cos φ.

RRB JE focus: simple circuit analysis, resonance frequency, power calculation.