A wire of resistance 12 ohm per metre is bent to form a complete circle of radius 10 c.m.the resistance between its two diametrically opposite point A and B
the circumference is C = 2pi*r. Make sure your answer is in meters, not cm.
Opposite ends of the diameter are half that far apart.
Now just multiply that by 12.
R across A-B= R/2=(1/2)pie r rho=1/2(pie*10*0.1*12 = 0.6pie ohms.
Total resistance of wire = 12Ω×2π×10
−1
= 2.4π
Resistance of each half =
2
2.4π
=1.2π
and as about diameter both parts are in parallel
Req. =
2
1.2π
=0.6πΩ
To find the resistance between points A and B, we can consider the wire as a resistor. The given wire has a resistance of 12 ohms per meter.
First, we need to find the length of the wire forming the circle. The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius is 10 cm or 0.1 meters. Therefore, the total length of the wire forming the circle is:
C = 2π(0.1) = 0.2π meters.
Now, we can calculate the resistance between points A and B. Since A and B are diametrically opposite points, the length of the wire between them is equal to half the circumference of the circle:
Length between A and B = (0.2π) / 2 = 0.1π meters.
Next, we can calculate the resistance between A and B using the formula R = ρL / A, where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire. In this case, the resistivity ρ is given as 12 ohm per meter, and the length L is 0.1π meters.
Finally, the formula can be rearranged to solve for the resistance R:
R = ρL / A = (12 ohm/m)(0.1π meters) / A.
The value of A is not given in the question, so we cannot calculate the exact resistance between points A and B without additional information.