Resistance to Electric Current

1. Cross-sectional area: Wider conductors offer less resistance (like a wide hallway allows easier movement).
2. Length of conductor: Longer conductors have more resistance (like a longer hallway takes more time to cross).
3. Temperature: Increasing temperature typically increases resistance in metallic conductors.

Ohm's law states:

The potential difference across a metallic conductor is directly proportional to the current flowing through it, provided that the temperature remains constant.

Mathematically:

$V \propto I \Rightarrow V = IR$

1. Linear resistor: Resistance remains constant regardless of voltage.
2. Non-linear resistor: Resistance changes with applied voltage (does not obey Ohm's Law).

Subtypes:

• Fixed resistor: Value is set during manufacturing and cannot be changed during its usage.

  

• Variable resistor (Potentiometer): Resistance can be adjusted during use.

  

Resistors are in series when connected end-to-end:

$R_{eq} = R_1 + R_2 + R_3 + \dots + R_n$

Voltage across each resistor:

$V = IR_1 + IR_2 + IR_3 + \dots + IR_n = I(R_1 + R_2 + R_3 + \dots + R_n)$

In parallel, all resistors share the same voltage:

$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}$

Total current:

$I = I_1 + I_2 + I_3 + \dots + I_n$

Example 2

Given two resistors of 3Ω and 5Ω:

In series:

$R = R_1 + R_2 = 3\,\Omega + 5\,\Omega = 8\,\Omega$

In parallel:

$\frac{1}{R} = \frac{1}{3} + \frac{1}{5} = \frac{5 + 3}{15} = \frac{8}{15} \Rightarrow R = \frac{15}{8} = 1.875\,\Omega$

The Wheatstone bridge is used to determine an unknown resistance.

It consists of four resistors $R_1, R_2, R_3, R_4$ connected in a closed loop. A galvanometer (G) is connected between the midpoints.

When the bridge is balanced:

$\frac{R_1}{R_2} = \frac{R_3}{R_4}$

No current flows through the galvanometer when the ratio of resistances in one pair equals the other.

An electric circuit is a system of electrical components connected by conductors (wires), forming a complete path for current to flow.

• Branches: Elements like resistors, voltage sources, etc.
• Nodes: Points where conductors meet.
• Circuit analysis: Involves finding voltages and currents when sources are known.

Current in a resistor follows Ohm's law, but in a voltage source, the current is determined by the rest of the circuit.