Network Theory
KVL and KCL, network theorems, transient and steady-state analysis, resonance and two-port parameters.
About this subject
Network Theory is about finding voltages and currents in circuits of resistors, capacitors, inductors and sources. It builds from Kirchhoff's laws to systematic methods (nodal and mesh analysis), network theorems (Thevenin, Norton, superposition, maximum power transfer), transients in RC and RL circuits, resonance, and two-port networks.
The subject rewards simplifying before solving. A Thevenin equivalent, a symmetry argument or a star-delta transformation can turn a page of simultaneous equations into two lines.
Solved questions
Each question is a practice problem written for this portal at GATE standard. Try it first, then open the full derivation, and read the note on the idea behind it.
- NAT Maximum power delivered to a load from a Thevenin source Network theorems · 1 mark
- NAT Capacitor voltage after one time constant in a series RC circuit Transient analysis · 1 mark
- NAT Resistance across the body diagonal of a cube of 1-ohm resistors Equivalent resistance · 2 marks
- NAT Bandwidth of a series RLC resonant circuit Resonance · 2 marks
Key formulas
The results these questions lean on most. Know what each symbol means, and when each one applies.
| What | Formula |
|---|---|
| Maximum power transfer | $R_L = R_{th}$, giving $P_{max} = V_{th}^2 / (4R_{th})$ |
| First-order charging | $v(t) = V_f + (V_i - V_f)\,e^{-t/\tau}$, with $\tau = RC$ or $L/R$ |
| Series RLC resonance | $\omega_0 = 1/\sqrt{LC}$, $\;Q = \dfrac{1}{R}\sqrt{L/C}$, $\;BW = R/L$ rad/s |
| Parallel RLC resonance | $Q = R\sqrt{C/L}$ - the reciprocal form |
| Quality factor and bandwidth | $BW = \omega_0 / Q$ |
| Star to delta | $R_{ab} = (R_aR_b + R_bR_c + R_cR_a)/R_c$ |
| Voltage divider | $v_2 = v\,R_2/(R_1 + R_2)$ |
How to prepare
- Reduce the network first: Thevenin equivalents, symmetry and source transformations.
- For every transient, write down three things before any algebra: the initial value, the final value and the time constant.
- Keep series and parallel resonance formulas side by side - they are easy to mix up because they are reciprocals.
- Check units and limiting cases: what happens as a resistor goes to zero or to infinity?
Common traps
Each of these costs marks every year. The questions above are built to catch them.
- Forgetting that at maximum power transfer only half the source voltage reaches the load.
- Using the discharge form of an exponential for a charging capacitor.
- Using the parallel-RLC quality factor for a series circuit.
- Trying to reduce a bridge or a cube with series and parallel steps alone.