Circuit Diagram Physics Example 3

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Example 3

medium

A circuit diagram shows three resistors:

R_1 = 2 \text{ } \Omega

in series with a parallel combination of

R_2 = 6 \text{ } \Omega

and

R_3 = 3 \text{ } \Omega

. A

12 \text{ V}

battery powers the circuit. What is the total current?

Solution

1
Parallel combination: $\frac{1}{R_p} = \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6}$ , so $R_p = 2 \text{ } \Omega$ .
2
Total resistance: $R_T = R_1 + R_p = 2 + 2 = 4 \text{ } \Omega$ . Current: $I = \frac{V}{R_T} = \frac{12}{4} = 3 \text{ A}$

Answer

I = 3 \text{ A}

Reading circuit diagrams requires identifying which components are in series and which are in parallel. Systematically simplifying the circuit step by step leads to the total resistance.

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A simplified drawing of an electrical circuit using standardized symbols for components like batteries, resistors, switches, and bulbs.

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