Introduction

This will be a basic introduction to direct current (DC) circuits. This post will supplement other posts on the site where we discuss basic circuitry. This is not meant to be a comprehensive look at DC circuits, just an overview in case you are unfamiliar.

See where these topics will be used:
Solar Installation Series – Part 1: Solar Power System – Design and Planning
DC Circuits – Series vs Parallel

Terms and Definitions

• Direct Current (DC) = A circuit where the electricity flows in only one direction. This circuit is common for battery-operated devices and car electrical systems.
• Alternating Current (AC) = A circuit where the electricity reverses direction in a sinusoidal wave at a specific frequency (60 Hz in U.S., 50 Hz in Europe and other places). Most commonly found in homes and businesses.
• Resistance (R) = the opposition of the flow of electricity. Measured in Ohms
• Current (I) = the flow of electricity through a circuit. Measured in Amperes
• Voltage (V) = the difference in electrical potential between two points, measured in volts.
• Ohm (Ω) = unit measure of resistance in a circuit.
• Ampere (A) = unit measure of current flow through a circuit, also know as an amp.
• Series = a circuit where the negative side of one component is connected to the positive of the next component.
• Parallel = a circuit where the positive side of each component is connected together and the negative side of each component is connected together.
• Equivalent Resistance (R_eq) = the total resistance of the circuit.

Ohm’s Law

V = IR

Ohm’s law states that voltage drop is equal to current times resistance. Of course, as with every equation, you can rearrange the equation to find the missing components. A popular graphic for this is the Ohm’s Law Triangle.

Basic Circuit Examples:

Example 1:

In the above example, there is a 12 V DC power source and a 150 Ω resistor. With these two values we can calculate the current flow in the circuit. Since we are looking for current (I), we need to divide Voltage by Resistance. I = (V/R). Substituting the values we get, I = (12/150). This results in 0.080 A, or 80 mA.

Example 2:

In this example, we have a 24 V power supply and a known current of 4.8 mA. What is the value of the resistor? The first thing you should do is convert the mA into Amps, which is needed for the equations. To do that, divide 4.8/1000, which will give
0.0048 A.

Next, we put these values into the Ohm’s law equation to get the value of the resistor in ohms. R = V/I. Plugging in the known values gives R = 24 V/0.0048 A, which equals 5000 Ω, or 5 kΩ.

Equivalent Resistance:

The last topic in this post will be about equivalent resistance. Equivalent resistance is the total resistance of a circuit. This is used to simplify the circuit so it is easier to find the other values in the circuit, such as voltage or current. The way we calculate the equivalent resistance is different depending on the circuit, and sometimes it can be a combination of the two.

Series Circuit

For a circuit in a series, which means that everything is on the same line and the current only has one path to follow, the equivalent resistance is the total value of all the resistors on that line.

To solve this for the equivalent resistance, you just need to add the values of resistors R1, R2, and R3. R_eq = 15 kΩ + 30 kΩ + 10 kΩ. That gives us an R_eq = 55 kΩ. Now you can solve for the current as you did above. The circuit can now be simplified to look like the one in Figure DC-5.

Parallel Circuit

In a parallel circuit, there are different branches that the current could go through. As a result, the formula for the equivalent resistance is a little more complicated. For parallel circuits you are adding together the inverse of the resistance values, which results in the inverse of the equivalent resistance. To get the actual equivalent resistance, you have to take the inverse of that value.

(1/R_eq = 1/R1 + 1/R2 + 1/R3) or (R_eq^-1 = R1^-1 + R2^-1 + R3^-1)

Plugging the values into the equation we get: 1/R_eq = (1/15 kΩ) + (1/30 kΩ) + (1/10 kΩ).
1/R_eq = 0.2 kΩ. To find R_eq we need to take the inverse of the 0.2 kΩ. (1/0.2) = 5 kΩ. Our simplified circuit is shown in Figure DC-7:

One thing to note is that the total resistance of a parallel circuit will be LESS than the value of the smallest resistor. In the example circuit, the smallest resistor is 10 kΩ, but the total resistance for the whole circuit is just 5 kΩ.

Thank You

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