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Parallel DC Circuits Practice Worksheet With Answers
24 questions By Tony R. Kuphaldt
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Question 4 of 24
The equation for calculating total resistance in a parallel circuit (for any number of parallel resistances) is sometimes written like this:
$$R_{total} = (R_1^{-1} + R_2^{-1} + ...R_n^{-1})^{-1}$$
Re-write this equation in such a way that it no longer contains any exponents.
Reveal answer$$R_{total} = \frac {1}{\frac{1}{R_1}+\frac{1}{R_2}+...\frac{1}{R_n}}$$
Notes:This question is an exercise in basic algebra, specifically the meaning of negative exponents.
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Question 5 of 24
Manipulate this equation to solve for resistor value R1, given the values of R2 and Rparallel:
$$R_{parallel} = \frac {R_1R_2}{R_1+R_2}$$
Then, give an example of a practical situation where you might use this new equation.
Reveal answer$$R_1 = \frac {R_2R_{parallel}}{R_2-R_{parallel}}$$
I’ll let you figure out a situation where this equation would be useful!
Notes:This question is really nothing more than an exercise in algebraic manipulation.
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Question 6 of 24
The formula for calculating total resistance of three parallel-connected resistors is as follows:
$$R = \frac {1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}$$
Algebraically manipulate this equation to solve for one of the parallel resistances (R1) in terms of the other two parallel resistances (R2 and R3) and the total resistance (R). In other words, write a formula that solves for R1 in terms of all the other variables.
Reveal answer$$R_1 = \frac {1}{\frac{1}{R}-(\frac{1}{R_2}+\frac{1}{R_3})} \ \ \ \ \ \ \ \ \ or \ \ \ \ \ \ \ \ \ R_1 = \frac {1}{\frac{1}{R}-\frac{1}{R_2}-\frac{1}{R_3}}$$
Notes:This question is nothing more than practice algebraically manipulating equations. Ask your students to show you how they solved it, and how the two given answers are equivalent.
