Exercises: Parallel Circuits

Work through each section in order. Show all steps: find R_eq, then branch currents, then verify with KCL.

Grade 11·21 problems·~30 min·OpenStax Physics (High School)·section·sec-19-3

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Fluency Practice

Two resistors, $R_1 = 6\ \Omega$ and $R_2 = 12\ \Omega$ , are connected in parallel. Calculate the equivalent resistance using the product-over-sum shortcut.

Three resistors — $R_1 = 20\ \Omega$ , $R_2 = 30\ \Omega$ , $R_3 = 60\ \Omega$ — are connected in parallel. Calculate the equivalent resistance.

Which of the following must always be true for the equivalent resistance of any parallel combination of resistors?

The equivalent resistance is less than the smallest individual resistor.

The equivalent resistance equals the average of the individual resistances.

The equivalent resistance increases as more resistors are added in parallel.

The equivalent resistance equals the sum of the reciprocals of each resistance.

Three resistors ( $R_1 = 20\ \Omega$ , $R_2 = 30\ \Omega$ , $R_3 = 60\ \Omega$ ) are connected in parallel to a 12 V source. What is the current through $R_2$ ?

Using the same parallel circuit ( $R_1 = 20\ \Omega$ , $R_2 = 30\ \Omega$ , $R_3 = 60\ \Omega$ , $V = 12\ \text{V}$ ), the branch currents are $I_1 = 0.60\ \text{A}$ , $I_2 = 0.40\ \text{A}$ , $I_3 = 0.20\ \text{A}$ . What is the total current from the source?

$1.20\ \text{A}$ — the sum of all branch currents.

$0.40\ \text{A}$ — the average of the three branch currents.

$0.20\ \text{A}$ — the current through the smallest branch.

$0.60\ \text{A}$ — the current through the largest branch.

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Exercises: Parallel Circuits

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Fluency Practice