Question

Seven resistances are connected as shown in the given figure. The equivalent resistance between A and B is

• A. $3 \Omega$
• B. $4 \Omega$
• C. $4.5 \Omega$
• D. $15 \Omega$

Answer 1

Answer: (B)

$4 \Omega$

Answer 2

Equivalent resistance of $R_1 \, and \, R_2$ (in parallel) is given by $R' = \frac {6 \times 6}{6 + 6} = 3 \Omega$ Equivalent resistance of $R_5 \, and \, R_7$ (in parallel) \, \, \, \, \, R' ' = \frac {10 \times 10}{10 + 10} = 5 \Omega Now, the circuit is reduced to Now, this circuit can be shown as it is balanced $\bigg(\frac {5}{3} = \frac {5}{3}\bigg)$ Total resistance between AB $R_{AB} = \frac {(5 + 3)(5 +3)}{(5 + 3)+(5 +3)}$ $= \frac {8 \times 8}{8 + 8 }= 4 \Omega$