When working with electronics, understanding how to use the principles of circuit analysis is crucial. Circuit analysis is the study of how electrons flow through a circuit and how to manage and control that flow.
Circuit analysis can be applied to circuits that have direct current (DC) only, alternating current (AC) only, or both DC and AC. When analyzing a circuit that has both DC and AC components, both types of circuits must be analyzed separately.
When there is only a direct current component in the circuit, then the mathematics for analyzing the circuit is very straightforward. You can even solve for all of the necessary components using just one variable: voltage.
When there are only alternating currents in the circuit, then again, the math becomes simpler. You can solve for all of the necessary components using just one variable: resistance.
When there are both DC and AC components in a circuit, however, things become more complicated. In order to analyze such a circuit, you must first split it up into two separate components: one that contains only DC components and one that contains only AC components.
Calculate current magnitude
Now that you know the voltage and resistance, you can calculate the current through the resistor. The formula you will use is current (I) = voltage (V) divided by resistance (R).
Since you are given the voltage and resistance, you only need to find the current. First, convert the resistance from ohms to amperes by dividing by one thousand: 20 Ω = 0.02 A. Then, divide 12 V by this new value of A: 0.12 / 0.02 = 6 A. This is the magnitude of the current in the 6-A resistor!
The direction of current in a circuit depends on which way you follow wires from one node to another. In this case, we are following wires out of the node with a 6-A resistor, so the current is flowing out of the node.
Calculate current direction
Now that you have the magnitude of the current in a circuit, you can calculate the direction of the current. The direction of the current is determined by which wire has more resistance.
If the higher resistance wire runs clockwise around the circle, then the current flows clockwise around the circle as well. If the higher resistance wire runs counterclockwise around the circle, then the current flows counterclockwise around the circle as well.
It is important to note that if both wires have equal resistance, then there is no way to determine which way the current flows. In this case, you must break out your electronics knowledge and assess which wire is attached to what object in order to determine flow.
Your job is now to apply this knowledge to your circuit and determine what currents flow clockwise or counterclockwise.
Use the triangle equation
The last thing you need to determine is the current in the 20 Ω resistor. You have the voltage across the resistor and the voltage across the parallel circuit, so you can use the triangle equation to solve for current.
This equation uses three of the four values of a right triangle (side length, angle, and one bisector) to find the fourth value (area). Here, side length = voltage across resistor, angle = resistance of resistor, one bisector = voltages across resistors in parallel circuit. Area = current in circuit.
Using your given information, you can substitute into this equation to get your answer.
Break down the problem into small pieces
Now let’s look at how we can determine the magnitude and direction of the current in the 20 Ω resistor. We will do this by breaking down the problem into smaller pieces.
First, let’s assume that there is no current in the 20 Ω resistor. What would be the voltage across it? Since there is no current flowing through it, there would be no voltage across it. It would be similar to having a short circuit, where there is zero voltage drop.
Second, let’s assume that there is a constant current in the 20 Ω resistor. What would be the voltage across it? Since there is a constant current flowing through it, there would be a constant voltage across it. It would be similar to having an open circuit, where there is zero voltage drop.
Third, what if we combine these two cases? Let’s assume that there is no current in any of the other resistors except for the 2 Ω resistor and that all of the currents in those two resistors are flowing in opposite directions (i.e., one points north and the other points south). What would be the magnitude and direction of the current in the 20 Ω resistor? Since all of these other resistors have a net north-south flow of current, then this must represent an east-west flow of current (opposite to them). The total east-west flow through all of these resistors must equal zero since they are adding up all of these flows and finding a difference; therefore, only west-east flows can pass through this resistor.
First-order approximation for AC
When the voltage across a resistor is changing with time, as it does in an AC circuit, you can make a first-order approximation of the current depending on whether the current is in the direction of the voltage change or against it.
When the current is in the same direction as the voltage change (called lagging voltage), you can assume that the current is zero. The reason for this assumption is that, for a very short amount of time, the voltage across the resistor is constant.
Since there is no difference in voltage across the resistor during this short amount of time, there is no difference in current across the resistor during this time. Since there is no current flowing out of or into the battery during this very short time, there is no AC current flowing through your 20 Ω resistor.
When there is an increase in voltage (called leading voltage) across a resistor, you can assume that there is no net AC current flowing through it. The reason for this assumption is that, for a very short amount of time, there is no flow of electrons away from the battery due to positive charge on the top terminal and negative charge on bottom terminal.
Calculate current magnitude
The current magnitude can be calculated by taking the difference between the voltage and resistance, and multiplying that difference by the circuit frequency.
I=V-R*f, where I is the current magnitude, V is the voltage across the resistor, R is the resistance of the resistor, and f is the frequency of the circuit.
If you do not know either the voltage or resistance of a circuit element, you can still calculate its current magnitude. You just need to know the frequency of the circuit.
Bullet point: Calculate current direction
Now that we have calculated the current magnitude, we can now calculate which way the current flows through this resistor. The rule for calculating current direction in circuits is very simple: if there is a positive voltage across a component, then there is a positive current through it. If there is a negative voltage across a component, then there is a negative current through it.
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