Question

1. The given electric circuit is a part of an electrical device. Use the information given in the electric circuit diagram to calculate:
   1. Potential difference across the ends of resistor R₂.
   2. Value of resistor R₁.

2. Write the factors on which resistance of a conductor depends and derive the formula for resistance of a given conductor.

Answer 1

i. I. Potential difference across R₂​:

Current in main branch = 2.0 A

Current through 4 Ω resistor = 1.5 A

⇒ Current through R₂ = 2.0 − 1.5 

= 0.5 A

Potential difference across 4 Ω:

V = IR

= 1.5 × 4

= 6 V

Since R₂ is in parallel with a 4 Ω resistor:

`V_(R_2)` = 6 V

II. Value of R₁​:

Apply KVL in the outer loop:

Battery voltage = 12 V

Voltage drop across:

2 Ω resistor:

V = 2 × 2

= 4 V

Parallel section = 6 V

Let drop across R₁ = V₁

12 = V₁ + 6 + 4

⇒ V₁ = 2 V

R₁ = `V_1/I`

= `2/2`

= 1 Ω

ii. Resistance ∝ Length:

R ∝ L

R ∝ `1/A`

R ∝ `L/A`

R = `rho L/A`

Factors affecting the resistance are length (L), area of cross-section (A), nature of material (resistivity, ρ), and temperature.