Question

What will be the equivalent resistance between the two points A and D?

• A. $30\, \Omega$
• B. $40\, \Omega$
• C. $10\, \Omega$
• D. $50\, \Omega$

Answer 1

Answer: (A)

$30\, \Omega$

Answer 2

Lower resistance on extreme left and upper resistance on extreme right are ineffective.
The resistance $R_2$ and $R_3$ are in series combination.
Therefore their equivalent resistance, $R' = R_2+R_3 = 10+10 = 20\, \Omega.$ Similarly, the resistance $R_5$ and $R_6$ are in series combination.
Therefore their equivalent resistance, R" $= R_5+R_6 = 10+10 = 20\, \Omega.$ Now the equivalent resistances R' and R'' are in parallel combination.
Therefore their equivalent resistance. $\, \, \, \, R''' =\frac{R' R''}{R'+R''}=\frac{20 \times 20}{20+20}=\frac{400}{40}=10\, \Omega.$
Thus equivalent resistance between A and D, R $= R_1+R'''+R_4=10+10+10=30\, \Omega$ ($\because$ series combination)