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A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ?
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A wire of resistance 20 ohms is bent to form a closed square. What is ...
If the wire is bent to form a square,then the resistance of the side of the square=20/4=5
Across the diagonal,
first calculate the resistance through the two sides that is
R1=5+5=10
then through the diagonal,R2=root over of(5^2+5^2)=5*root2
as R1 and R2 are parallel to each other,
1/R=1/R1+1/R2
1/R=1/10+1/5*root2
1/R=(root2+root2)/10*root2
1/R=2*root2/10*root2
root2 cancelled in both,hence
1/R=2/10
1/R=1/5
R=5
Hope it helped you.
Across the diagonal,
first calculate the resistance through the two sides that is
R1=5+5=10
then through the diagonal,R2=root over of(5^2+5^2)=5*root2
as R1 and R2 are parallel to each other,
1/R=1/R1+1/R2
1/R=1/10+1/5*root2
1/R=(root2+root2)/10*root2
1/R=2*root2/10*root2
root2 cancelled in both,hence
1/R=2/10
1/R=1/5
R=5
Hope it helped you.
Community Answer
A wire of resistance 20 ohms is bent to form a closed square. What is ...
Solution:
To find the resistance across the diagonal of the square, we need to first understand how resistance is distributed in a wire.
Resistance in a Wire:
Resistance in a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Mathematically, we can represent resistance as:
R = (ρ * L) / A
Where,
- R is the resistance
- ρ (rho) is the resistivity of the material of the wire
- L is the length of the wire
- A is the cross-sectional area of the wire
Resistance in a Square:
When a wire is bent to form a square, its length and resistivity remain the same. However, the cross-sectional area changes.
Resistance across the Diagonal:
To find the resistance across the diagonal of the square, we can consider two resistors connected in parallel. Each resistor represents one side of the square.
Calculating the Resistance:
Given that the resistance of the wire is 20 ohms, we can find the length and cross-sectional area of the wire.
Length of the Wire:
Since the wire forms a square, each side of the square is equal to the length of the wire. Therefore, the length of the wire is L = 4s, where s is the length of one side of the square.
Cross-Sectional Area of the Wire:
The wire has a rectangular cross-section, and its width and height are equal to the sides of the square. Therefore, the cross-sectional area of the wire is A = s^2.
Substituting the Values:
Substituting the values in the resistance formula, we get:
R = (ρ * L) / A
R = (ρ * 4s) / (s^2)
R = 4ρ / s
Since the wire is bent to form a square, the length of the wire is equal to the sum of all sides of the square. Therefore, s = L/4.
Substituting the value of s, we get:
R = 4ρ / (L/4)
R = 16ρ / L
Thus, the resistance across the diagonal of the square is equal to 16 times the resistance of the wire. Therefore, the resistance across the diagonal is 16 * 20 = 320 ohms.
To find the resistance across the diagonal of the square, we need to first understand how resistance is distributed in a wire.
Resistance in a Wire:
Resistance in a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Mathematically, we can represent resistance as:
R = (ρ * L) / A
Where,
- R is the resistance
- ρ (rho) is the resistivity of the material of the wire
- L is the length of the wire
- A is the cross-sectional area of the wire
Resistance in a Square:
When a wire is bent to form a square, its length and resistivity remain the same. However, the cross-sectional area changes.
Resistance across the Diagonal:
To find the resistance across the diagonal of the square, we can consider two resistors connected in parallel. Each resistor represents one side of the square.
Calculating the Resistance:
Given that the resistance of the wire is 20 ohms, we can find the length and cross-sectional area of the wire.
Length of the Wire:
Since the wire forms a square, each side of the square is equal to the length of the wire. Therefore, the length of the wire is L = 4s, where s is the length of one side of the square.
Cross-Sectional Area of the Wire:
The wire has a rectangular cross-section, and its width and height are equal to the sides of the square. Therefore, the cross-sectional area of the wire is A = s^2.
Substituting the Values:
Substituting the values in the resistance formula, we get:
R = (ρ * L) / A
R = (ρ * 4s) / (s^2)
R = 4ρ / s
Since the wire is bent to form a square, the length of the wire is equal to the sum of all sides of the square. Therefore, s = L/4.
Substituting the value of s, we get:
R = 4ρ / (L/4)
R = 16ρ / L
Thus, the resistance across the diagonal of the square is equal to 16 times the resistance of the wire. Therefore, the resistance across the diagonal is 16 * 20 = 320 ohms.
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A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ?
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A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ?.
A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of resistance 20 ohms is bent to form a closed square. What is the resistance across the diagonal of the square ?.
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