Question 1

Which equation correctly represents the total resistance $$R_{total}$$ for three resistors $$R_1$$, $$R_2$$, and $$R_3$$ connected in parallel?

Accepted Answer

$$R_{total} = \dfrac{1}{\dfrac{1}{R_1$} + \dfrac{1}{R_2$} + \dfrac{1}{R_3$}}$$

Question 2

If two resistors, $$R_1 = 4$$\ \Omega$$ and R_2$ = 6\ \Omega$$, are connected in parallel, what is the total resistance $$R_{total}$$?

Accepted Answer

$$R_{total} = 2.4\ \Omega$$

Question 3

Which of the following statements about resistors in parallel is correct?

Accepted Answer

The total resistance is always less than the smallest individual resistor.

Question 4

Given three resistors in parallel: $$R_1 = 2$$\ \Omega$$, R_2$ = 3\ \Omega$$, $$R_3 = 6$$\ \Omega$$, calculate R$$_{total}$$.

Accepted Answer

$$R_{total} = 1\ \Omega$$

Question 5

If one resistor in a parallel circuit is removed, what happens to the total resistance?

Accepted Answer

It increases.

Question 6

A parallel circuit has three resistors: $$R_1 = 10$$\ \Omega$$, R_2$ = 20\ \Omega$$, $$R_3 = 30$$\ \Omega$$. What is the total resistance?

Accepted Answer

$$R_{total} = 5.45\ \Omega$$

Question 7

Which of the following is the correct step to find the total resistance in a parallel circuit?

Accepted Answer

Add the reciprocals of each resistance, then take the reciprocal of the sum.

Question 8

If $$R_1 = 5$$\ \Omega$$ and R_2$ = 10\ \Omega$$ are in parallel, what is the current through $$R_1 if $$the total current is $$3\ A$$?

Accepted Answer

$$I_1 = 2$$\ A$$

Question 9

Which real-world application best illustrates the use of parallel resistors?

Accepted Answer

Christmas tree lights that stay lit even if one bulb burns out.

Question 10

If three identical resistors of $$12\ \Omega$$ each are connected in parallel, what is the total resistance?

Accepted Answer

$$R_{total} = 4\ \Omega$$

Question 11

A parallel circuit has resistors $$R_1 = 8$$\ \Omega$$ and R_2$ = 24\ \Omega. $$What is the total resistance?

Accepted Answer

$$R_{total} = 6\ \Omega$$

Question 12

Which formula would you use to find the total resistance for $$n$$ resistors in parallel?

Accepted Answer

$$R_{total} = \dfrac{1}{\dfrac{1}{R_1$} + \dfrac{1}{R_2$} + \cdots + \dfrac{1}{R_n}}$$

Question 13

If the total resistance in a parallel circuit is $$2\ \Omega$$ and one resistor is $$4\ \Omega$$, what could be the value of the second resistor?

Accepted Answer

$$4\ \Omega$$

Question 14

Why is the total resistance in a parallel circuit always less than the smallest resistor?

Accepted Answer

Because adding more paths allows more current to flow.

Question 15

A technician needs a total resistance of $$3\ \Omega$$ using two resistors in parallel. If one resistor is $$6\ \Omega$$, what should be the value of the second resistor?

Accepted Answer

$$6\ \Omega$$

Calculating Equivalent Resistance in Parallel Circuits

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