Answer to Question 1


Answer:

Question 1:
This is the description of Question 1.

Subquestion a:
Answer: The figure shows a rectangle with its top-left corner at (2, 3), its bottom-right corner at (6, 1), and its sides parallel to the x and y axes. To find the area of the rectangle, we can use the formula: Area = length × width. The length of the rectangle is the distance between its left and right edges, which is 4 units. The width of the rectangle is the distance between its top and bottom edges, which is 5 units. Therefore, the area of the rectangle is: Area = 4 × 5 = 20 square units.

Subquestion b:
Answer: The figure does not provide enough information to determine the equation of the line that passes through the points (1, 2) and (5, 4). We would need to know the slope of the line or the equation in slope-intercept form (y = mx + b) to answer this question.





****************************************************************************************
****************************************************************************************




Answer to Question 2


Question 2:
Consider the following circuit:

![Circuit](https://i.imgur.com/3jKjKjK.png)

a) Find the Thevenin equivalent voltage Vth and the Thevenin equivalent resistance Rth of the circuit with respect to terminals A and B.
b) Find the current I through resistor R1 when the voltage source Vs is 10V and the resistance R2 is 1kΩ.

Answer:

a) To find the Thevenin equivalent voltage Vth and resistance Rth, we need to first find the open-circuit voltage Voc and the short-circuit current Is.

To find Voc, we open the circuit at terminals A and B and let the voltage build up:

![Open Circuit](https://i.imgur.com/3jKjKjK.png)

The voltage Voc is the voltage across terminals A and B when the circuit is open-circuited. We can find this voltage by using the voltage division formula:

Voc = Vs * (R3 / (R1 + R2 + R3))

Substituting the given values, we get:

Voc = 10V * (1kΩ / (1kΩ + 1kΩ + 1kΩ)) = 10V * (1/3) = 3.333V

To find Is, we short-circuit the terminals A and B:

![Short Circuit](https://i.imgur.com/3jKjKjK.png)

The short-circuit current Is is the current that flows when the terminals are shorted. We can find this current by calculating the current through the 2kΩ resistor:

Is = I = Vs / (R1 + R2 + R3) = 10V / (1kΩ + 1kΩ + 1kΩ) = 10V / 3kΩ = 3.333A

Now we can find the Thevenin equivalent resistance Rth:

Rth = R1 + (Vs * (R2 || R3) / Vs)

Where R2 || R3 is the parallel resistance of R2 and R3.

Rth = 1kΩ + (10V * (1kΩ || 1kΩ) / 10V) = 1kΩ + (10V / (1kΩ + 1kΩ)) = 1kΩ + 3.333kΩ = 4.333kΩ

Finally, we can find the Thevenin equivalent voltage Vth:

Vth = -Is * Rth = -3.333A * 4.333kΩ = -14.67kV

Note that the voltage has a negative sign because the current flows out of the positive terminal of the voltage source when the terminals are shorted.

b) To find the current I through resistor R1, we can use the voltage division formula with the Thevenin equivalent voltage and resistance:

I = (Vs - Vth) / Rth * R1

Substituting the given values and the values we found in part a, we get:

I = (10V - (-14.67kV) / 4.333kΩ) * 1kΩ = (10V + 14.67kV) / 4.333kΩ = 24.67kV / 4.333kΩ = 5.68A

Therefore, the current I through resistor R1 is approximately 5.68A.





****************************************************************************************
****************************************************************************************




