Question

Which of the following is NOT a possible value for the total resistance of the resistor combinations with four $6$ ohm resistors?

• A. $24$ $\Omega$
• B. $12$ $\Omega$
• C. $8$ $\Omega$
• D. $6$ $\Omega$
• E. $1.5$ $\Omega$

Answer 1

Answer: (B)

$12$ $\Omega$

(1) When all four in series then equivalent resistance $R=6+6+6+6=24\Omega$

(2) When all four in parallel then equivalent resistance

$\frac{1}{R}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}$

or, $R=1.5\Omega$

(3) When two in series and two in parallel then equivalent resistance $R_1=6+6=12\Omega$

$\frac{1}{R_2}=\frac{1}{6}+\frac{1}{6}$

or, $R_2=3\Omega$

so $R=12+3=15\Omega$

(4) When two in parallel then other two in parallel also

$\frac{1}{R_1}=\frac{1}{6}+\frac{1}{6}$

or, $R_1=3\Omega$

$\frac{1}{R_2}=\frac{1}{6}+\frac{1}{6}$

or, $R_2=3\Omega$

$R=6\Omega$

(5) When three in parallel then one in series

$\frac{1}{R_1}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}$

or, $R_1=2\Omega$

$R=2+6=8\Omega$

Therefore, we dont find $12\Omega$ in any combination.