Answer to Question #121281 in Electric Circuits for Asif Sultan

Question

What is the right option of 179?
http://prntscr.com/swe1fz

Answer 1

Explanations & Calculations

• Electrical resistance of a material is given by R = $\frac{\rho l}{A}$
• Therefore a relationship for the given wire could be written using that as follows.

$\qquad\qquad \begin{aligned} \small 36 &= \frac{\rho \times l}{A} = \small kl \cdots(\frac{\rho}{A} \,\,\text{is constant}) \end{aligned}$

• This means the resistance of a segment of this wire depends on the length of the segment considered.

• Therefore, resistance of the 30⁰ segment (R₁)

$\qquad\qquad \begin{aligned} \small R_1 &= \small k\times \frac{30l}{360} = \small \frac{1}{12}kl = 3\Omega\\ \end{aligned}$

• Resistance of the remaining segment is (R₂ )

$\qquad\qquad \begin{aligned} \small R_2 &= \small \frac{11}{12}kl = \small 36-R_1 = 33 \Omega \end{aligned}$

• About AB, these two wires are in a parallel combination which equivalent to (R_e)

$\qquad\qquad \begin{aligned} \small R_e &= \small \frac{3\Omega\times33\Omega}{3\Omega+33\Omega}\\ &= \small \bold{2.75 \Omega} \end{aligned}$

• Answer (A)