Working Formula – All Experiments
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Working Formula
G = SR / (R − S)
Meaning of Symbols
G is galvanometer resistance, R is series resistance, and S is shunt resistance.
Example Question
During the half-deflection experiment, a series resistance R = 30 Ω and shunt resistance S = 10 Ω are used. Determine the galvanometer resistance G.
Given
- R = 30 Ω
- S = 10 Ω
Solution
G = SR / (R − S)
G = (10 × 30) / (30 − 10)
G = 300 / 20
Final Answer
G = 15 Ω
Try It Yourself
If R = 40 Ω and S = 10 Ω, determine G.
For finding unknown resistance:
X / R = l / (100 − l)
For finding specific resistance / resistivity:
ρ = Xπr² / L
Example Question
Using a meter bridge, X = 2 Ω is found for a specimen wire with radius r = 0.5 mm and length L = 1 m. Calculate its specific resistance ρ.
Given
- X = 2 Ω
- r = 0.5 mm = 0.0005 m
- L = 1 m
Formula
ρ = Xπr² / L
Calculation
ρ = Xπr² / L
ρ = 2 × π × (0.0005)² / 1
ρ = 2 × 3.1416 × 0.00000025
ρ = 0.0000015708 Ω·m
Final Answer
ρ ≈ 1.57 × 10⁻⁶ Ω·m
Try It Yourself
If X = 4 Ω, r = 1 mm and L = 2 m, determine ρ.
Answer: ρ = 4 × π × (0.001)² / 2 ≈ 6.28 × 10⁻⁶ Ω·m
Screw Gauge Reading → Radius → Resistivity
Example Question
A screw gauge gives the following readings for a specimen wire. Calculate the diameter and radius of the wire.
Given
- LSR = 0.5 cm
- CBR = 43
- Least Count = 0.01 cm
Meaning of Symbols
- LSR = 0.5 cm
- CBR = 43
- Least Count = smallest measurement value of the screw gauge
- D = diameter of the specimen wire
- r = radius of the specimen wire
Formula
D = LSR + (CBR × Least Count)
Step 1: Calculate Diameter
D = LSR + (CBR × Least Count)
D = 0.5 + (43 × 0.01)
D = 0.5 + 0.43
D = 0.93 cm
Step 2: Calculate Radius
r = D / 2
r = 0.93 / 2
r = 0.465 cm
Step 3: Calculate Specific Resistance / Resistivity
X = 0.4219 Ω
L = 86 cm
ρ = Xπr² / L
ρ = [0.4219 × 3.1416 × (0.465)²] / 86
ρ = [0.4219 × 3.1416 × 0.216225] / 86
ρ ≈ 0.00332 Ω·cm
Final Answer
ρ ≈ 0.00332 Ω·cm
Complete result: D = 0.93 cm; r = 0.465 cm; ρ ≈ 0.00332 Ω·cm
Meaning of Symbols
X is unknown resistance, R is known resistance, l is the balancing length, ρ is specific resistance / resistivity, r is the radius of the specimen wire, and L is the length of the specimen wire.
Example Question
In a meter bridge, the known resistance is R = 4 Ω and the balance point is l = 40 cm from the left end. Calculate the unknown resistance X.
Given
- X = unknown resistance
- R = 4 Ω
- l = 40 cm
Solution
X / R = l / (100 − l)
X / 4 = 40 / (100 − 40)
X = 4 × 40 / 60 = 160 / 60
Final Answer
X = 2.67 Ω (approximately)
Try It Yourself
If R = 6 Ω and l = 25 cm, determine X.
Working Formula
X = (P / Q) × R
Meaning of Symbols
X is unknown resistance, R is standard resistance, and P and Q are ratio arms.
Example Question
In a Post Office Box, P, Q and R are given. Determine the unknown resistance X.
Given
- P = 2
- Q = 1
- R = 5 Ω
Solution
X = (P / Q) × R
X = (2 / 1) × 5
X = 2 × 5
Final Answer
X = 10 Ω
Try It Yourself
If P = 3, Q = 2 and R = 4 Ω, determine X.