Question 1

In a circuit analysis, what is the definition of an 'essential branch'?

Accepted Answer

A branch that lies on at least one closed loop and contains at least one circuit element.

Question 2

How many independent Kirchhoff's Voltage Law (KVL) equations can be written for a planar circuit with $$b$$ branches and $$n$$ nodes?

Accepted Answer

$$b - n + 1$$

Question 3

Given a mesh with resistors $$R_1$$, $$R_2$$, and a voltage source $$V$$, which of the following is the correct KVL equation for the mesh current $$I$$ flowing clockwise?

Accepted Answer

$$V - R_1$ I - R_2$ I = 0$$

Question 4

In a circuit, if the mesh equation for Mesh 2 is $$-200 - 20I_2 + 9I_1 + I_3$ = 0$$, which of the following is the correct rearrangement for $$I_2$$?

Accepted Answer

$$I_2$$ = \frac{200 + 9I_1 + $$I_3$$}{-20}$$

Question 5

For a circuit with a $$20\Omega$$ resistor as the load, the Thevenin resistance $$R_{th}$$ seen by the load is calculated by:

Accepted Answer

Removing the $$20\Omega$$ resistor and calculating the equivalent resistance seen from its terminals.

Question 6

In Figure 2, a $$20V$$ voltage source is in series with a $$2\Omega$$ resistor and a $$4\Omega$$ resistor. What is the voltage $$V_o$$ across the $$4\Omega$$ resistor?

Accepted Answer

$$V_o = 13.33V$$

Question 7

For the circuit in Figure 3, if the voltage across the $$7\Omega$$ resistor is $$-2.71V$$, what is the direction of current through the resistor?

Accepted Answer

From right to left

Question 8

In a circuit with a dependent source, how do you calculate the power associated with the dependent source?

Accepted Answer

Multiply the value of the dependent source by the current through it, considering the correct sign convention.

Question 9

For the circuit in Figure 4, if Mesh 2 has a current $$I_2 = -17.5A$, what does the negative sign indicate?

Accepted Answer

The current flows in the opposite direction to the assumed mesh direction.

Question 10

For the circuit in Figure 5, if the current $$i_x = 0.5A$$ through a $$1.5\Omega$$ resistor, what is the voltage across the resistor?

Accepted Answer

$$V = 0.75V$$

Question 11

For the circuit in Figure 5, if the $$1.5\Omega$$ resistor is the load, what is the Thevenin resistance $$R_{th}$$ seen by the load?

Accepted Answer

$$R_{th} = 2.22\Omega$$

Question 12

For the circuit in Figure 6, if the Thevenin voltage $$V_{th}$$ with respect to terminals a and b is $$-25V$$, what does the negative sign indicate?

Accepted Answer

Terminal b is at a higher potential than terminal a.

Question 13

For the circuit in Figure 7, which of the following is a valid supermesh equation if a current source lies between Mesh 1 and Mesh 2?

Accepted Answer

$$V_1$$ - $$R_1$$ $$I_1$$ - $$R_2$$ $$I_2$$ + $$V_2$$ - $$R_3$$ $$I_3 = 0$ \ I_1$ - I_2$ = I_{source}$$

Question 14

What is the fundamental relationship between a load resistor $$R_L$$ and the circuit's Thevenin resistance $$R_{th}$$ for maximum power transfer?

Accepted Answer

$$R_L = R_{th}$$

Question 15

A real-world application: In a medical device powered by a battery, why is it important to match the load resistance to the Thevenin resistance of the battery circuit?

Accepted Answer

To ensure maximum power is delivered to the device for optimal operation.

Question 16

If a dependent voltage source in a circuit is defined as $$V_x = 2i$$, where $$i is $$the current through a $$5\Omega$$ resistor, and $$i = 3A$$, what is the power supplied by the dependent source if the current enters the positive terminal?

Accepted Answer

$$P = -18W$$

Question 17

In a circuit, if the Norton current $$I_N is $$found to be $$4A$$ and the Norton resistance $$R_N is$$ $$2\Omega$$, what is the open-circuit voltage across the terminals?

Accepted Answer

$$V_{oc} = 8V$$

Question 18

A $$10V$$ battery is connected to a load through a Thevenin resistance of $$5\Omega. $$What value of load resistance will receive maximum power?

Accepted Answer

$$R_L = 5\Omega$$

Question 19

If a circuit contains both independent and dependent sources, what is the correct procedure to find the Thevenin resistance?

Accepted Answer

Deactivate all independent sources and leave dependent sources active.

Study Notes: DC Circuits, Mesh and Nodal Analysis, and Thevenin’s Theorem

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