Ohm's Law & Combination of Resistors: Comprehensive NEET Physics Notes

1. Ohm's Law

1.1 Definition and Mathematical Expression

Ohm's Law states that the potential difference ( $V$ ) across the ends of a conductor is directly proportional to the current ( $I$ ) flowing through it, provided the temperature and other physical conditions remain constant. Mathematically, it is expressed as: $V = I R$

Where:

$V$ is the potential difference (volts, V)
$I$ is the current (amperes, A)
$R$ is the resistance (ohms, $Ω$ )

NEET Tip:

Always remember that Ohm's Law is only valid when the physical state (such as temperature) of the conductor remains unchanged.

Did You Know?

Georg Simon Ohm formulated this law in 1827, long before the discovery of electrons. Ohm’s Law forms the foundation for understanding electric circuits, a crucial part of the NEET syllabus.

2. Combination of Resistors

Resistors can be combined in two primary ways: series and parallel. Understanding how they affect the overall resistance is crucial for solving complex circuits.

2.1 Resistors in Series

When resistors are connected end-to-end, they are said to be in series. The current flowing through each resistor is the same, but the voltage across each resistor may differ.

Equivalent Resistance in Series

For resistors $R_{1}, R_{2}, R_{3}, \dots R_{n}$ connected in series, the total or equivalent resistance $R_{s}$ is given by: $R_{s} = R_{1} + R_{2} + R_{3} + \dots + R_{n}$

Key Points:

Current remains the same through all resistors.
Total voltage is the sum of the individual voltages across each resistor.

NEET Problem-Solving Strategy:

For series circuits, calculate the total resistance first to find the overall current using Ohm's Law, then analyze individual voltage drops. Practice similar questions regularly to enhance your problem-solving skills.

Common Misconception:

Students often believe that the voltage is the same across all resistors in a series circuit. Remember, it's the current that remains constant, not the voltage.

2.2 Resistors in Parallel

When resistors are connected such that each end is joined together, they are in parallel. The voltage across each resistor is the same, but the current may vary.

Equivalent Resistance in Parallel

For resistors $R_{1}, R_{2}, R_{3}, \dots, R_{n}$ connected in parallel, the reciprocal of the total or equivalent resistance $R_{p}$ is given by: $\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \frac{1}{R _{3}} + \dots + \frac{1}{R _{n}}$

Key Points:

Voltage remains the same across all resistors.
Total current is the sum of the individual currents through each resistor.

Real-life Application:

Parallel circuits are widely used in household wiring systems to ensure that each appliance receives the same voltage. This ensures that turning off one appliance doesn’t affect the others.

2.3 Series and Parallel Combination

In complex circuits, resistors may be connected in a combination of series and parallel. The key to solving these circuits is to break them down into smaller, manageable parts.

Visual Aid Suggestion:

Include diagrams illustrating the series and parallel combinations with arrows showing the direction of current flow to visualize how voltage and current distribute.

3. Practice Questions with Detailed Solutions

Question 1

Given: Three resistors with resistances $5Ω$ , $10Ω$ , and $15Ω$ are connected in series. Find the total resistance.

Solution: Since the resistors are in series, the total resistance $R_{s}$ is: $R_{s} = R_{1} + R_{2} + R_{3} = 5 + 10 + 15 = 30Ω$

Question 2

Given: Three resistors of $6Ω$ , $12Ω$ , and $18Ω$ are connected in parallel. Find the equivalent resistance.

Solution: For parallel combination: $\frac{1}{R _{p}} = \frac{1}{6} + \frac{1}{12} + \frac{1}{18} = \frac{6 + 3 + 2}{36} = \frac{11}{36}$ Thus, $R_{p} = \frac{36}{11} \approx 3.27Ω$

Question 3

Given: Find the current flowing through a resistor of $10Ω$ when a voltage of $20 V$ is applied across it.

Solution: Using Ohm's Law: $V = I R ⟹ I = \frac{V}{R} = \frac{20}{10} = 2 A$

Question 4

Given: Two resistors, $R_{1} = 4Ω$ and $R_{2} = 6Ω$ , are connected in parallel. Find the total resistance.

Solution: For parallel resistors: $\frac{1}{R _{p}} = \frac{1}{4} + \frac{1}{6} = \frac{3 + 2}{12} =$