Content

• To step
• Method 1 of 3: Series connection
• Method 2 of 3: Parallel connection
• Method 3 of 3: Mixed circuit
• A number of facts
• Tips

Would you like to know how to calculate the resistance in a series circuit, parallel circuit or a mixed circuit? If you don't want your circuits to burn out, for sure! This article shows you how to do this in a few short steps. Before you continue reading, it is good to realize that a resistor has no such things as an "entrance" and an "exit". The use of these terms is only intended to clarify the concept for beginners.

To step

Method 1 of 3: Series connection

1. What is it. Series-connected resistors are connected so that the "output" of one resistor is connected to the "input" of another, in the same circuit. Any resistance added to the circuit adds to the total resistance of the circuit.
   • The formula for calculating a total of n resistors connected in series is: R._eq = R.₁ + R₂ + .... R_n This simply means that the values ​​of all series-connected resistors have been added together. As an example, take the problem to find the total (equivalent) of the resistors, as shown in the image below.
   • In this example, R.₁ = 100 Ω and R.₂ = 300Ω connected in series. R._eq = 100 Ω + 300 Ω = 400 Ω

Method 2 of 3: Parallel connection

1. What is it. Parallel resistors are connected in such a way that the "inputs" of 2 or more resistors are connected to each other and so are the "outputs".
   • The equation for the combination of n parallel resistances is: R._eq = 1 / {(1 / R₁) + (1 / R₂) + (1 / R₃) .. + (1 / R_n)}
   • Here is an example where R.₁ = 20 Ω, R.₂ = 30 Ω, and R.₃ = 30 Ω.
   • The total resistance for all 3 parallel resistors is: R._eq = 1 / {(1/20) + (1/30) + (1/30)} = 1 / {(3/60) + (2/60) + (2/60)} = 1 / (7 / 60) = 60/7 Ω = approximately 8.57 Ω.

Method 3 of 3: Mixed circuit

1. What is it. A mixed circuit is any combination of series and parallel connections. Try to find the total resistance of the network as shown below.
   • We see that the resistors R.₁ and R.₂ connected in series. So their total resistance (let's write it as R._s) is: R._s = R.₁ + R₂ = 100 Ω + 300 Ω = 400 Ω.
   • Next we see that the resistors R.₃ and R.₄ connected in parallel with each other. So here is the total resistance (let's write it as R._p1): R._p1 = 1/{(1/20)+(1/20)} = 1/(2/20)= 20/2 = 10 Ω
   • Finally, we see that the resistors R.₅ and R.₆ are also connected in parallel. So their total resistance (let's write it as R._p2) is: R._p2 = 1/{(1/40)+(1/10)} = 1/(5/40) = 40/5 = 8 Ω
   • So now we have a circuit with the resistors R._s, R._p1, R._p2 and R.₇ connected in series. These can now simply be added together to find the total resistance R._eq of the entire network of circuits R._eq = 400 Ω + 10 Ω + 8 Ω + 10 Ω = 428 Ω.

A number of facts

1. Try to understand what resistance is. Any material that conducts current has a resistivity, which is the resistance of that material to electrical current.
2. Resistance is measured in ohm. The symbol for ohms is Ω.
3. Different materials have different resistance.
   • For example, copper has a resistivity of 0.0000017 (Ω / cm)
   • Ceramic has a resistivity of approximately 10 (Ω / cm)
4. The higher the number, the greater the resistance to the electric current. You can see that copper, commonly used for power wire, has a very low resistivity. Ceramics, on the other hand, have such a high resistance that it is an excellent insulator.
5. How you connect multiple resistors together makes a lot of difference to the ultimate power of a network of resistors.
6. V = IR. This is Ohm's Law, discovered by Georg Ohm in the first half of the 19th century.
   • V = IR: Voltage (V) is the product of current (I) * resistance (R).
   • I = V / R: Current is the quotient of voltage (V) ÷ resistance (R).
   • R = V / I: Resistance is the quotient of voltage (V) ÷ current (I).

Tips

• Remember, when resistors are connected in parallel, the current is transported across multiple paths, so the sum of the resistance is less than that of each path. When resistors are connected in series, current must pass through each resistor, so the resistors are added together for the total resistance.
• The total resistance is always less than the smallest resistance in a parallel connection; it is always greater than the greatest resistance in a series circuit.