Problem: 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.

🤓 Based on our data, we think this question is relevant for Professor Younes' class at GWU.

FREE Expert Solution

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.

R57 = 10 + 2 = 12Ω

R57 is in parallel with R6

R567 = (12)(6)/(12 + 6) = 4Ω

R567 is in series with R8

R5678 = 4 + 8 = 12Ω

Problem Details

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.

Frequently Asked Questions

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.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Younes' class at GWU.