Combining Resistors in Series & Parallel Video Lessons

Concept

# Problem: What is the equivalent resistance between points a and b in the figure? (Figure 1)Please show work.

###### FREE Expert Solution

Let's label the resistors as:

Equivalent resistance for 2 resistors in parallel:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}\frac{{\mathbf{R}}_{\mathbf{1}}{\mathbf{R}}_{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{1}}\mathbf{+}{\mathbf{R}}_{\mathbf{2}}}}$

Equivalent resistance for resistors in series:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{n}}}}$

Resistors 1 and 2 are in parallel:

R12 = (30)(45)/(30 + 45) = 18Ω

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###### Problem Details

What is the equivalent resistance between points a and b in the figure? (Figure 1)