Question

Three resistors are connected to form the sides of a triangle ABC as shown below. The resistance of side AB is 40 ohms, of side BC 60 ohms and of side CA 100 ohms. The effective resistance between the point A and B in ohms is:

• A. $50$
• B. $64$
• C. $32$
• D. $100$

Answer 1

Answer: (C)

$32$

To calculate resistance between A and B, we can treat resistors between BC and AC to be in series,

There equivalent hence is,

$R^{\prime }=R_{BC}+R_{AC}⟹R^{\prime }=60+100=160\Omega$

Now this equivalent resistor $R^{\prime }$ is in parallel with $R_{AB}$.

Equivalent of $R^{\prime }$ and $R_{AB}$ can be calculated using formula,

$R_{EQ}=\frac{R^{\prime }{R}_{AB}}{R_{AB}+R^{\prime }}⟹R_{EQ}=\frac{160\times 40}{160+40}=32\Omega$