Answer all questions, write your answers in the box provided and submit this paper immediately after the test.

We are given two charges, $q_1 = 4.5 \times 10^{-9} \text{ C}$ and $q_2 = -2.8 \times 10^{-9} \text{ C}$, and the distance between them, $r = 3.2 \text{ m}$. We need to find the electrostatic force $F$. Coulomb's constant $k = 8.99 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2$.
The formula for electrostatic force is:

Rounding to three significant figures, $F = 1.11 \times 10^{-8} \text{ N}$.

The correct option is (A).
The electrostatic force is $\boxed{\text{A) } 1.11 \times 10^{-8} \text{ N}}$.

We are given the separation distance $d = 5.33 \text{ mm} = 5.33 \times 10^{-3} \text{ m}$ and the potential difference $V = 600 \text{ V}$. We need to find the magnitude of the electric field $E$.
The formula for the electric field between parallel plates is:

Rounding to three significant figures, $E = 1.13 \times 10^5 \text{ V/m}$.

The correct option is (A) or (D), as they are identical.
The magnitude of the electric field is $\boxed{\text{A) } 1.13 \times 10^5 \text{ V/m}}$.

We are given the charge $Q = 7.2 \times 10^{-3} \text{ C}$ and the capacitance $C = 6.0 \text{ µF} = 6.0 \times 10^{-6} \text{ F}$. We need to find the voltage $V$.
The relationship is $Q = CV$, so we can rearrange it to find $V$:

The calculated voltage is $1200 \text{ V}$. This value is not among the options (A) $14 \text{ V}$, (B) $12 \text{ V}$, (C) $15 \text{ V}$, (D) $20 \text{ V}$.
It is highly probable that there is a typo in the question, and the charge was intended to be $7.2 \times 10^{-5} \text{ C}$ (which is $72 \text{ µC}$). If we assume this typo:

Assuming this common type of typo, the answer matches option (B).

The correct option, assuming a typo in the charge value ($7.2 \times 10^{-5} \text{ C}$ instead of $7.2 \times 10^{-3} \text{ C}$), is (B).
The voltage required is $\boxed{\text{B) } 12 \text{ V}}$.

We are given the area $A = 7.60 \text{ cm}^2 = 7.60 \times 10^{-4} \text{ m}^2$, the separation distance $d = 1.80 \text{ mm} = 1.80 \times 10^{-3} \text{ m}$, and the potential difference $V = 20.0 \text{ V}$. The permittivity of free space $\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2/\text{N} \cdot \text{m}^2$.
The formulas are:
Electric field: $E = \frac{V}{d}$
Capacitance: $C = \epsilon_0 \frac{A}{d}$

Rounding to three significant figures, $E = 1.11 \times 10^4 \text{ V/m}$.

Rounding to three significant figures, $C = 3.74 \text{ pF}$.

The calculated values are $E = 1.11 \times 10^4 \text{ V/m}$ and $C = 3.74 \text{ pF}$. This matches option (B).

The correct option is (B).
The electric field is $\boxed{\text{B) } 1.11 \times 10^4 \text{ V/m}}$ and the capacitance is $\boxed{\text{B) } 3.74 \text{ pF}}$.

We are given the internal resistance $r = 2 \Omega$ and the external resistance $R = 6 \Omega$.
The efficiency $\eta$ of a cell is given by the ratio of power dissipated in the external resistor to the total power produced by the cell:

The correct option is (D).
The efficiency of the cell is $\boxed{\text{D) } 75\%}$.

We are given the diameter $D = 100.0 \text{ µm} = 100.0 \times 10^{-6} \text{ m}$, which means the radius $R = 50.0 \times 10^{-6} \text{ m}$. The surface charge density $\sigma = 100.0 \text{ µC/m}^2 = 100.0 \times 10^{-6} \text{ C/m}^2$. The permittivity of free space $\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2/\text{N} \cdot \text{m}^2$.
The formulas are:
Surface area of a sphere: $A = 4\pi R^2$
Total charge: $Q = \sigma A$
Electric flux (Gauss's Law): $\Phi_E = \frac{Q}{\epsilon_0}$

The calculated charge is $3.14 \times 10^{-12} \text{ C}$ and the flux is $0.355 \text{ N} \cdot \text{m}^2/\text{C}$. None of the provided options match these values. The options for charge are in the order of $10^{-3} \text{ C}$, and the options for flux are in the order of $10^{11} \text{ N} \cdot \text{m}^2/\text{C}$. There appears to be a significant discrepancy in the problem statement's units or the options provided.
However, if we assume a typo in the diameter and surface charge density such that the charge is $2.54 \times 10^{-3} \text{ C}$ (from option B), then the flux would be:

This still does not match the flux values in the options ($7.25 \times 10^{11}$).
Given the options, it's impossible to derive a consistent answer from the problem statement. I will state the calculated values based on the problem as written. Since I must choose an option, and all options for flux are $7.25 \times 10^{11}$ or $6.25 \times 10^{11}$, and the charge values are $X \times 10^{-3}$, I will assume there are multiple typos and select the option that is most commonly chosen in such scenarios, which is often the first one with a common flux value. However, this is a guess.
Let's assume the question intended for the flux to be $7.25 \times 10^{11} \text{ N} \cdot \text{m}^2/\text{C}$ and then calculate the charge from that.
$Q = \Phi_E \epsilon_0 = (7.25 \times 10^{11} \text{ N} \cdot \text{m}^2/\text{C}) (8.85 \times 10^{-12} \text{ C}^2/\text{N} \cdot \text{m}^2) = 6.416 \text{ C}$. This is not $10^{-3}$.

This question is fundamentally flawed. I will provide the calculation based on the given values and state that the options do not match. If forced to choose, I cannot logically select one. I will state the correct calculation and then indicate the discrepancy.

Based on the provided values:
The charge on the sphere is $\boxed{3.14 \times 10^{-12} \text{ C}}$ and the total electric flux leaving the sphere is $\boxed{0.355 \text{ N} \cdot \text{m}^2/\text{C}}$.
Note: These calculated values do not match any of the given multiple-choice options, indicating a potential error in the question's parameters or the options themselves.

The top branch has resistors $30 \Omega$, $20 \Omega$, and $50 \Omega$ in series.

The bottom branch has resistors $60 \Omega$, $20 \Omega$, and $30 \Omega$ in series.

The middle branch has a single resistor of $25 \Omega$.

The three branches ($R_{top}$, $25 \Omega$, and $R_{bottom}$) are in parallel.

The voltage source is $V = 20 \text{ V}$. Using Ohm's Law:

The calculated equivalent resistance is $14.47 \Omega$ and the total current is $1.382 \text{ A}$. None of the options match these values.
Let's re-examine the circuit diagram and options. The options for equivalent resistance are $120 \Omega$, $200 \Omega$, $100 \Omega$, $150 \Omega$. These are much larger than my calculated $14.47 \Omega$. The options for current are $0.2 \text{ A}$ or $0.4 \text{ A}$. My calculated current is $1.382 \text{ A}$.
There is a significant discrepancy. It's possible the diagram is interpreted differently or there's a typo in the options.
If the resistors were in series, $R_{eq} =