Resistance of metal wire of length 1m is 26ohm at 2celcies if diameter of wire is 0.4m what will be the resistivity of metal at this temperature?

Question

Answer

Calculating Resistivity of Metal Wire

Given Data:
- Length of wire (L) = 1m
- Resistance (R) = 26 ohm
- Temperature (T) = 2 °C
- Diameter of wire (d) = 0.4m

Step 1: Calculate the cross-sectional area of the wire
- Radius (r) = d/2 = 0.4m / 2 = 0.2m
- Area (A) = πr^2 = π(0.2)^2 = 0.04π m^2

Step 2: Calculate the resistivity of the metal
- Resistivity (ρ) = R * (A / L) = 26 * (0.04π / 1) = 1.04π ohm*m

Step 3: Convert temperature to Kelvins
- T(K) = T(°C) + 273 = 2 + 273 = 275K

Step 4: Apply temperature correction to resistivity
- α = 0.0039/°C (temperature coefficient of resistivity for the metal)
- ρ(T) = ρ(0) * [1 + α(T - T0)] = 1.04π * [1 + 0.0039(275 - 20)] = 1.04π * 2.09

Step 5: Calculate the final resistivity of the metal at 2°C
- ρ(T) ≈ 2.17π ohm*m

Therefore, the resistivity of the metal wire at a temperature of 2°C is approximately 2.17π ohm*m.

Answer

L=1m R= 26 ohm d=0.4m ,r=0.2m resistivity =? resistivity =RA÷l therefore A= 22÷7×0.2×0.2=0.88/7msquare R=26×0.88/7=3.268m =3.27m

Similar Class 10 Doubts

The resistance of a metal wire of length 1m is 26 ohm at 20 degree Celsius . If the diameter of the wire is 0.3 mm , what will be the resistivity of the metal at that temperature ?

Resistance of metal wire of length 2m is 40ohm.If the diameter of the wire is 0.3mm,what will be the resistivity of the metal at that temperature?

A copper wire has a diameter of 0.5 mm and resistivity of 1.6 ×10^-8ohm meter .what will be the length of this wire to make its resistance 10 ohm ?how much does the resistance change if the diameter is doubled?

Resistance of a metal wire of length 1m is 0.84 ohm at 20 C. If the diameter of the wire is 0.2 m . Calculate it's resistivity.?

Resistance of a metal wire of length 1m is 0.84 ohm at 20 C. If the diameter of the wire is 0.2 m . Calculate it's resistivity.?

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Grammar Advanced

English Grammar Basic

Top Courses for Class 10

Top Courses for Class 10

Suggested Free Tests

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company