Simple KVL, KCL and Ohm's Law problems

In summary, the value of Ro can be determined by using the equations V = iR, KCL, and KVL in the given circuit. By calling the current through Ro as I_o and the current through the 20 ohm resistor as I_1, it can be determined that I_o + I_1 = 16A and -192V - (20 ohm)(I_o) + (20 ohm)(I_1) = 0. From this, it can be concluded that 192 = I_o Ro, allowing for the value of Ro to be determined.
  • #1
oygad
1
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simple04_fg.png


Given: In the circuit shown above, 192 V is dropped across the unknown resistor, Ro.

Required: Determine the value of Ro.

V = iR, KCL and KVL
I really don't know where to go on this one. I know that the right side's voltage will need to add up to zero, but that's about all I know.
 
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  • #2
Call the current through the resistor [tex]R_o[/tex], [tex]I_o[/tex] and call the current through the sole [tex]20 \Omega[/tex] resistor [tex]I_1[/tex] then we know that:

[tex]I_o + I_1 = 16A[/tex] and starting from [tex]R_o[/tex] and going clockwise we have [tex]-192V - (20 \Omega) (I_o) + (20 \Omega)(I_1)=0[/tex]

Subsequently, [tex]192 = I_o R_o[/tex].

3 equations and 3 unknowns.
 
  • #3


First, let's define some terms. KVL stands for Kirchhoff's Voltage Law, which states that the sum of all voltages in a closed loop must equal zero. KCL stands for Kirchhoff's Current Law, which states that the sum of all currents entering and exiting a node must equal zero. Ohm's Law states that the voltage across a resistor is equal to the current through the resistor multiplied by the resistance.

In this circuit, we only have one unknown resistor (Ro) and one known voltage (192 V). Using Ohm's Law, we can rewrite the equation as V = iRo. We also know that the current entering the node on the left must equal the current exiting the node on the right, according to KCL. Therefore, we can set up the following equation:

iRo = iR1 + iR2

Where R1 and R2 are the resistors on the left and right sides of the circuit, respectively. We can simplify this equation by factoring out the current (i):

i(Ro - R1 - R2) = 0

Since the current (i) cannot be equal to zero (otherwise there would be no voltage drop across Ro), we can set the expression in parentheses equal to zero:

Ro - R1 - R2 = 0

Now we have two equations and two unknowns (Ro and R1), so we can solve for Ro. We can use KVL to find the voltage drop across R1:

192 V = iR1

Substituting this into the previous equation, we get:

Ro - (192 V/i) - R2 = 0

We can rearrange this equation to solve for Ro:

Ro = (192 V/i) + R2

Since we do not have enough information to solve for i, we cannot determine the exact value of Ro. However, we can say that Ro must be greater than (192 V/i) since it is being added to R2, which is a positive value. Therefore, the minimum value of Ro is (192 V/i) + 0, which is (192 V/i).
 

What is KVL?

KVL stands for Kirchhoff's Voltage Law, which states that the sum of the voltages around a closed loop in a circuit must equal zero. This law is based on the principle of conservation of energy.

What is KCL?

KCL stands for Kirchhoff's Current Law, which states that the sum of the currents entering and exiting a node (or junction) in a circuit must equal zero. This law is based on the principle of conservation of charge.

What is Ohm's Law?

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them. It can be represented by the equation I = V/R, where I is current in amperes, V is voltage in volts, and R is resistance in ohms.

How do I apply KVL, KCL, and Ohm's Law to solve simple circuit problems?

To solve simple circuit problems using KVL, KCL, and Ohm's Law, you must first identify the unknown values (e.g. voltage, current, or resistance) and the known values in the circuit. Then, you can use the appropriate equations and principles to set up and solve a system of equations to find the unknown values.

What are the limitations of KVL, KCL, and Ohm's Law?

KVL, KCL, and Ohm's Law are based on ideal conditions and may not accurately represent real-world situations. Additionally, they assume linear relationships between voltage, current, and resistance, which may not always be the case. They also do not account for other factors such as temperature or non-ohmic components. In more complex circuits, these laws may not provide enough information to solve the problem and additional laws and techniques may be necessary.

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