Ohm's Law & Kirchhoff's Laws Notes

Last reviewed 16 Sept 2026 · 7 min read

Basic quantities

Quantity	Symbol	Unit	Relation
Charge	Q	coulomb (C)	Charge of an electron $= 1.602 \times 1 0^{- 19}$ C
Current	I	ampere (A)	$I = \frac{Q}{t}$ — rate of flow of charge
Potential difference (voltage)	V	volt (V)	Work done per unit charge, $V = \frac{W}{Q}$
Electromotive force (EMF)	E	volt	Energy supplied per unit charge by a source
Resistance	R	ohm (Ω)	Opposition to current
Conductance	G	siemens (S)	$G = 1/ R$
Power	P	watt (W)	Rate of energy conversion
Energy	W	joule (J); kWh ("unit")	$1 kWh = 3.6 \times 1 0^{6}$ J

Conventional current flows from positive to negative terminal outside a source (opposite to electron flow).

Resistance and resistivity

FormulaResistance of a conductor

R = ρ \frac{L}{A}

$ρ$ = resistivity (Ω·m) — copper about $1.72 \times 1 0^{- 8}$ Ω·m, aluminium about $2.8 \times 1 0^{- 8}$ Ω·m at 20 °C; $L$ = length; $A$ = cross-sectional area. Conductivity $σ = 1/ ρ$ .

Resistance increases with length, decreases with area, depends on material and temperature.

Effect of temperature

R_{t} = R_{0} (1 + α_{0} t)

$α_{0}$ = temperature coefficient of resistance at 0 °C.
Metals — positive α (resistance increases with temperature); copper about 0.0043 per °C at 0 °C.
Carbon, semiconductors, electrolytes, insulators — negative α.
Alloys such as manganin, constantan, eureka — very small α → used in standard resistors and shunts.

Ohm's law

At constant temperature (and other physical conditions), the current through a conductor is directly proportional to the potential difference across it:

V = I R

Limitations: not applicable to non-linear devices — diodes, transistors, arc lamps, electrolytes, gas discharge tubes, thyristors; and to conductors whose temperature changes significantly.

Power and energy

FormulaPower and energy

P = V I = I^{2} R = \frac{V ^{2}}{R}

W = P t; Energy (kWh) = \frac{Power (W) \times time (h)}{1000}

Series and parallel resistors (summary)

Series: $R_{e q} = R_{1} + R_{2} + \dots$ ; same current; voltages divide.
Parallel: $\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$ ; same voltage; currents divide. Two resistors: $R_{e q} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$ .

Divider rules

FormulaVoltage and current dividers

Voltage divider (series): $V_{1} = V \frac{R _{1}}{R _{1} + R _{2}}$

Current divider (two parallel branches): $I_{1} = I \frac{R _{2}}{R _{1} + R _{2}}$

Kirchhoff's laws

Kirchhoff's current law (KCL)

The algebraic sum of currents at a node (junction) is zero — total current entering = total current leaving. Based on conservation of charge.

\sum I = 0

Kirchhoff's voltage law (KVL)

The algebraic sum of all voltages (EMFs and voltage drops) around any closed loop is zero. Based on conservation of energy.

\sum V = 0 (\sum E = \sum I R)

Sign convention

Going through a source from − to + → rise (+); from + to − → drop (−).
Going through a resistor in the direction of assumed current → drop (−IR); against → rise.
If a computed current is negative, its actual direction is opposite to that assumed.

Downloaded from civilgyantests.com · Not for resale. Verify every code clause and date against the official source.

Basic quantities

Resistance and resistivity

Effect of temperature

Ohm's law

Power and energy

Series and parallel resistors (summary)

Divider rules

Kirchhoff's laws

Kirchhoff's current law (KCL)

Kirchhoff's voltage law (KVL)

Sign convention

This chapter is in the syllabus of