Solving Circuit Homework with KCL and KVL: V = IR Equation Method"

[Novark]

Homework Statement

Homework Equations

KCL / KVL
V = IR

The Attempt at a Solution

[Edit] Nevermind, I got it. I don't know what the heck I was trying to do.

For future reference, in case someone needs to know, this is how it's solved:

V1 = 4*I
V2 = -2*I

-10 + V1 - 8 - V2 = 0
V1 - V2 = 18
(4*I) - (-2*I) = 18
6*I = 18
I = 3

V1 = 4*(3) = 12 V
V2 = -2*(3) = -6 V

 

[anathema]

To solve this problem, we can use Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). KCL states that the sum of currents entering a node must equal the sum of currents leaving the node. KVL states that the sum of voltage drops around a closed loop must equal the sum of voltage sources in that loop.

First, we label the currents in the circuit as I1 and I2. Using KCL at the top node, we can write the equation -10 + V1 - 8 - V2 = 0, where V1 and V2 are the voltage drops across the 10 ohm and 8 ohm resistors, respectively.

Next, using KVL around the loop on the right side, we can write the equation V1 - V2 = 18, where V1 and V2 are the voltage drops across the 4 ohm and 2 ohm resistors, respectively.

Simplifying these equations, we get 4*I1 - 2*I2 = 10 and I1 - I2 = 9. Solving these equations simultaneously, we get I1 = 3 amps and I2 = 2 amps.

Finally, using Ohm's Law (V = IR), we can calculate the voltage drops across each resistor: V1 = 4*I1 = 12 volts and V2 = -2*I2 = -4 volts. Therefore, the voltage at the top node is 12 volts and the voltage at the bottom node is -6 volts.

 

[kerimek]

The KCL (Kirchhoff's Current Law) and KVL (Kirchhoff's Voltage Law) are two essential tools in solving circuit problems. KCL states that the sum of all currents entering a node must equal the sum of all currents leaving the node. KVL states that the sum of all voltages around a closed loop in a circuit must be equal to zero. These laws can be used to create equations and solve for unknown variables, such as voltage (V), current (I), and resistance (R).

In this problem, we are using the V = IR equation method to solve for the unknown current in the circuit. By applying KCL at the node between V1 and V2, we can set up the equation -10 + V1 - 8 - V2 = 0. By applying KVL around the closed loop, we can also set up the equation V1 - V2 = 18. By substituting V1 = 4I and V2 = -2I into these equations, we can solve for I. Once I is known, we can then use the V = IR equation to solve for the voltage at each node, V1 and V2.

In conclusion, the KCL and KVL laws, along with the V = IR equation method, are powerful tools in solving circuit problems and can be applied to a wide range of circuit configurations. It is important for scientists and engineers to have a strong understanding of these laws in order to effectively analyze and design electronic circuits.