Current:

$\overline{){\mathbf{i}}{\mathbf{=}}\frac{\mathbf{V}}{{\mathbf{R}}_{\mathbf{e}\mathbf{q}}}}$

Equivalent resistance for resistors in series:

$\overline{){{\mathbf{R}}}_{\mathbf{e}\mathbf{q}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{2}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{3}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{n}}}}$

Equivalent resistance for resistors in parallel:

$\overline{)\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{e}\mathbf{q}}}{\mathbf{=}}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{n}}}}$

Label the resistors as follows:

Resistors 5 and 7 are in series.

R_{57} = 10 + 2 = 12Ω

R_{57} is in parallel with R_{6}

R_{567} = (12)(6)/(12 + 6) = 4Ω

R_{567} is in series with R_{8}

R_{5678} = 4 + 8 = 12Ω

Consider the circuit shown in (Figure 1).

What is the current through the battery? Express your answer to two significant figures and include the appropriate units.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Combining Resistors in Series & Parallel concept. You can view video lessons to learn Combining Resistors in Series & Parallel. Or if you need more Combining Resistors in Series & Parallel practice, you can also practice Combining Resistors in Series & Parallel practice problems.

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