In one line
Kirchhoff's Current Law (KCL) says the total current entering a node equals the total current leaving it, and Kirchhoff's Voltage Law (KVL) says the algebraic sum of voltages around any closed loop is zero.
Explained simply
Think of a node as a road junction: every car that drives in must drive out, because cars cannot pile up or vanish there. Charge behaves the same way, so current in = current out. For voltage, think of walking around a hill and coming back to your starting point: whatever height you climbed, you must also descend, so the net change in height is zero. Voltage is "electrical height", so around a closed loop the rises equal the drops.
Technically, KCL follows from conservation of charge: \( \sum I = 0 \) at any node. KVL follows from conservation of energy: \( \sum V = 0 \) around any closed path (EMF rises = IR drops).
How it works
- Mark all nodes and loops. Assign a current with an assumed direction to every branch.
- KCL at a node: take currents entering as positive and leaving as negative (or the reverse, but stay consistent).
- KVL in a loop: pick a direction (say clockwise). Going from \( - \) to \( + \) of a source is a rise (+E); going through a resistor in the direction of current is a drop (\( -IR \)).
- Write as many independent equations as there are unknowns and solve them.
- If a current comes out negative, its actual direction is opposite to the one you assumed. The magnitude is still correct.
Key formula
KCL: \( \sum I_{\text{in}} = \sum I_{\text{out}} \) at a node. KVL: \( \sum E = \sum IR \) around a closed loop.
\( I \) = current in amperes (A), \( E \) = source EMF in volts (V), \( R \) = resistance in ohms (\( \Omega \)), \( IR \) = voltage drop in volts.
Quick example
KCL: 5 A enters a node; 2 A leaves through one branch. The current \( I \) in the other leaving branch is \( 5 = 2 + I \Rightarrow I = 3 \) A.
KVL: a 12 V battery feeds 2 \( \Omega \) and 4 \( \Omega \) in series. Going round the loop: \( 12 - 2I - 4I = 0 \Rightarrow I = 2 \) A. Drops are 4 V and 8 V, which add to 12 V as KVL demands.
Common mistakes
- Mixing sign conventions inside one loop, for example treating one resistor drop as + and another as \( - \) while moving in the same direction.
- Writing KCL at a node using voltages instead of currents, or forgetting a branch connected to the node.
- Thinking a negative answer means a mistake. It only means the assumed direction was wrong.
How MU asks it
Usually a 5-mark theory question ("State and explain KCL and KVL") or the first step of a numerical on loop/branch currents worth 7–10 marks. For full marks: state both laws in words, write them as equations, draw a small node and loop diagram with signs marked, state your sign convention, and show the equations before solving. Mention that KCL comes from conservation of charge and KVL from conservation of energy.