Q: Given the circuit in the first image, what is the equivalent capacitance of the combination of the 25 $$\muF $$and 87 $$\muF $$capacitors in series?

$$C_{eq} = \frac{25 \times 87}{25 + 87} = 19.6\ \mu\mathrm{F}$$

Q: For the resistor circuit in the second image, what is the equivalent resistance of the parallel combination of the 33 $$\Omega$$ and 62 $$\Omega$$ resistors?

$$R_{eq} = \frac{33 \times 62}{33 + 62} = 21.2\ \Omega$$

Question 1

According to Coulomb’s Law, what is the mathematical expression for the force between two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r in $$vacuum?

Accepted Answer

$$F = k_e \frac{q_1$ q_2$}{r^2$}$$

Question 2

If the charge on one particle is doubled while the distance between two charges remains constant, how does the electromagnetic force between them change?

Accepted Answer

The force doubles.

Question 3

If the distance between two point charges is doubled, what happens to the force between them according to Coulomb’s Law?

Accepted Answer

The force becomes one-fourth as large.

Question 4

Which particle experiences the greater electromagnetic force: a charge $$q or a $$charge $$2q$$ placed near each other?

Accepted Answer

Both experience forces of equal magnitude but opposite direction.

Question 5

What is the difference between a point charge and a test charge in the context of electric fields?

Accepted Answer

A point charge creates an electric field, while a test charge is used to measure the field without disturbing it.

Question 6

How do electric field lines indicate the sign of a charge?

Accepted Answer

Field lines point away from positive charges and toward negative charges.

Question 7

Which of the following best describes capacitance?

Accepted Answer

The ability of a system to store electric charge per unit voltage.

Question 8

How does increasing the area of the plates in a parallel plate capacitor affect its capacitance?

Accepted Answer

Capacitance increases.

Question 9

What is the effect of inserting a dielectric material between the plates of a capacitor?

Accepted Answer

It increases the capacitance.

Question 10

Given the circuit in the first image, what is the equivalent capacitance of the combination of the 25 $$\muF $$and 87 $$\muF $$capacitors in series?

Accepted Answer

$$C_{eq} = \frac{25 	imes 87}{25 + 87} = 19.6\ \mu\mathrm{F}$$

Question 11

For the capacitor circuit in the first image, what is the total equivalent capacitance between the terminals?

Accepted Answer

$$C_{total} = 73 + 19.6 = 92.6\ \mu\mathrm{F}$$

Question 12

For the resistor circuit in the second image, what is the equivalent resistance of the parallel combination of the 33 $$\Omega$$ and 62 $$\Omega$$ resistors?

Accepted Answer

$$R_{eq} = \frac{33 	imes 62}{33 + 62} = 21.2\ \Omega$$

Question 13

For the resistor circuit in the second image, what is the total current supplied by the battery?

Accepted Answer

$$I = \frac{4.5}{75 + 21.2} = 0.047\ \mathrm{A}$$

Question 14

In the third image, which law would you use to write equations for the currents $$I_1$$, $$I_2$$, and $$I_3 in $$the circuit?

Accepted Answer

Kirchhoff’s Junction and Loop Rules

Question 15

What is the time constant $$	au$$ for an RC circuit with $$R = 710\ \Omega$$ and $$C = 18\ \mu\mathrm{F}$$?

Accepted Answer

$$	au = RC = 710 	imes 18 	imes 10$$^{-6}$$ = 0.0128\ \mathrm{s}$$

Question 16

A battery with emf $$\mathcal{E} = 12\ \mathrm{V}$$ and internal resistance $$r = 0.3\ \Omega is $$connected to a $$1.3\ \Omega$$ load. What is the terminal voltage $$V_{term}$$?

Accepted Answer

$$V_{term} = 12 - I r$$, where $$I = \frac{12}{1.3 + 0.3} = 7.5\ \mathrm{A}$$, so $$V_{term} = 12 - (7.5 	imes 0.3) = 9.75\ \mathrm{V}$$

Question 17

Which of the following best describes Ohm’s Law?

Accepted Answer

$$V = IR$$

Question 18

What is the energy stored in a capacitor with $$C = 18\ \mu\mathrm{F}$$ and $$V = 4.6\ \mathrm{V}$$?

Accepted Answer

$$U = \frac{1}{2} C V^2$ = \frac{1}{2} 	imes 18 	imes 10$$^{-6}$$ 	imes (4.6)^2$ = 1.90 	imes 10$$^{-4}$$\ \mathrm{J}$$

Step-by-Step Guidance for Circuit Analysis: Capacitors and Resistors

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