Question

What is the equivalent resistance of three resistors with values, 1.2

Answer 1

Explanations & Calculations

• Equivalent resistance of a set of series connected resistors is given by,

$\qquad\qquad \small R_{eq} = \small R_1+R_2+R_3\cdots$

• Equivalent resistance of a set of parallel connected resistors is given by,

$\qquad\qquad \frac{1}{R_{eq}} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} \cdots$

• A set of 3 resistors could be connected in 3 different ways

1^st case: All three are series connected

$\qquad\qquad \begin{aligned} \small R_{eq} &= \small 1.2\Omega+1.2\Omega+1.2\Omega\\ &= \small \bold{3.6\Omega} \end{aligned}$

2^nd case: All three are parallel connected

$\qquad\qquad \begin{aligned} \small \frac{1}{R_{eq}} &= \small \frac{1}{1.2\Omega}+\frac{1}{1.2\Omega}+\frac{1}{1.2\Omega}\\ &= \small \frac{1.2}{3} \\ &=\small \bold{ 0.4\Omega} \end{aligned}$

3^rd case: Only two of them parallel & that connected to the other one

• Equivalent of the parallel 2 resistors,

$\qquad\qquad \begin{aligned} \small R_{eq1} &= \small \frac{1.2\Omega}{2}\\ &= \small \bold{0.6\Omega} \end{aligned}$

• Then the final equivalent resistance = 1.2$\Omega$ + R_eq1 = $\small\bold{1.8\Omega}$