Question

Four resistances of each 20 ohm are connected to form a square $A,B,C,D$. The resultant resistance between the corners $AC$ and the resistance between $AB$ are:

• A. 40$\Omega$, 15$\Omega$
• B. 15$\Omega$, 40$\Omega$
• C. 15$\Omega$, 20$\Omega$
• D. 20$\Omega$, 15$\Omega$

Answer 1

The correct option is D 20$\Omega$, 15$\Omega$

From fig 1:
The resistance AB and AC are in series having a total resistance 40 ohm. And the resistance AD and DC are in series having a total resistance 40 ohm. Now these two are in parallel. SO the total resistance between AC is $\left(40||40\right)=20$ohm.
From fig 2:
The resistance AD, DC, CB are in series having a total resistance 60 ohm which is in parallel with AB. So the total resistance between AB is $\left(60||20\right)=15$ ohm.