Q: Two identical spheres of mass $$5.0\ \mathrm{g}$$ are suspended from $$1.0\ \mathrm{m}$$ threads and each is given the same positive charge. If the angle between the threads is $$4.1^\circ$$, what is the correct formula to find the charge $$q on $$each sphere? (Assume $$k = 9.0 \times 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$.)

$$q = \sqrt{\dfrac{mg r^2$ \tan \theta}{k}}$$

Question 1

Given three circuits, each with identical batteries, resistors, and capacitors, which circuit will have the shortest time constant for charging the capacitor if Circuit 1 has two resistors in series, Circuit 2 has two resistors in parallel, and Circuit 3 has a single resistor? (Recall $$	au = RC$$ for a single resistor and capacitor.)

Accepted Answer

Circuit 2

Question 2

For the same three circuits, what is the correct ranking of the time required for the capacitor to charge completely, from shortest to longest?

Accepted Answer

2 \u003c 1 \u003c 3

Question 3

If the equivalent resistance of a circuit is $$2R$$ and the capacitance is $$C$$, what is the time constant $$	au$$ for the circuit?

Accepted Answer

$$	au = 2RC$$

Question 4

Two identical spheres of mass $$5.0\ \mathrm{g}$$ are suspended from $$1.0\ \mathrm{m}$$ threads and each is given the same positive charge. If the angle between the threads is $$4.1^\circ$$, what is the correct formula to find the charge $$q on $$each sphere? (Assume $$k = 9.0 	imes 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$.)

Accepted Answer

$$q = \sqrt{\dfrac{mg r^2$ 	an 	heta}{k}}$$

Question 5

In the scenario with two charged spheres, which force is responsible for the horizontal separation of the spheres?

Accepted Answer

Electrostatic repulsion

Question 6

If the mass of each sphere is doubled in the charged spheres experiment, how does the required charge $$q to $$maintain the same angle $$	heta$$ change?

Accepted Answer

It increases by a factor of $$\sqrt{2}$$

Question 7

A capacitor in an RC circuit is initially uncharged. After closing the switch, what is the voltage across the capacitor as a function of time $$t$$?

Accepted Answer

$$V_C(t) = V_0$ (1 - e$$^{-t/RC}$$)$$

Question 8

If the resistance in an RC circuit is halved, how does the time constant $$	au$$ change?

Accepted Answer

It is halved

Question 9

In the charged spheres experiment, if the length of the thread is increased to $$2.0\ \mathrm{m}$$ while keeping all other parameters the same, what happens to the separation between the spheres?

Accepted Answer

It increases

Question 10

Which of the following best describes the physical meaning of the time constant $$	au in an RC $$circuit?

Accepted Answer

The time it takes for the capacitor to reach about 63% of its maximum charge

Question 11

A real-world defibrillator uses a capacitor to deliver a pulse of energy to a patient. If the resistance of the patient's body is $$1000\ \Omega$$ and the capacitor is $$200\ \mu\mathrm{F}$$, what is the time constant $$	au$$?

Accepted Answer

$$	au = 0.2\ \mathrm{s}$$

Question 12

If the angle $$	heta$$ between the threads in the charged spheres experiment is increased, what must happen to the charge $$q on $$each sphere to maintain equilibrium?

Accepted Answer

The charge must increase

Question 13

Which of the following is a correct application of Newton's second law in the vertical direction for the charged spheres experiment?

Accepted Answer

$$T \cos 	heta = mg$$

Question 14

In an RC circuit, if the capacitance is doubled while the resistance remains constant, how does the time constant $$	au$$ change?

Accepted Answer

It doubles

Question 15

A $$5.0\ \mathrm{g}$$ sphere is suspended and charged as in the experiment. If the gravitational acceleration $$g is $$increased, what happens to the equilibrium angle $$	heta$$ for the same charge $$q$$?

Accepted Answer

The angle decreases

Capacitor Charging Time & Electrostatic Equilibrium Problems – PHYS 202 Exam Prep

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