Exam

JIPMER

Year

2007

Subject

Physics

Chapter

Current Electricity

JIPMER 2007 · Physics · Current Electricity

When a wire of uniform cross-section a , length l and resistance R...

When a wire of uniform cross-section $a$, length $l$ and resistance $R$ is bent into a complete circle, resistance between two of diametrically opposite points will be

Step-by-step solution

When wire is bent to form a complete circle then $2 \pi r=R \Rightarrow r=\frac{R}{2 \pi}$ Resistance of each semicircle $=\pi r=\frac{\pi R}{2 \pi}=\frac{R}{2}$ Thus, net resistance in parallel combination of two semicircular resistance $R^{\prime}=\frac{\frac{R}{2} \times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{\frac{R^2}{4}}{R}=\frac{R}{4}$