4 Ways to Calculate Total Resistance in a Circuit

There are two ways to assemble electronic components. A series circuit connects components without branches, while a parallel circuit connects components with branches. The way the resistors are arranged determines the total resistance in the circuit.

Step

Method 1 of 4: Series Circuit

Step 1. Identify the series circuit

A series circuit is a branchless circuit. All resistors and other components are assembled in one line.

Step 2. Add up all the resistance values

In a series circuit, the total resistance is equal to the sum of all the resistances. Each resistor carries the same amount of current so that each resistor works as we expect.

For example, a series circuit has a 2 (Ohm) resistor, a 5 resistor, and a 7 resistor. The total resistance of the circuit is 2 + 5 + 7 = 14

Step 3. Calculate the amount of current or voltage

If you don't know the resistance of each resistor, use Ohm's Law: V = IR, or voltage = current x resistance. The first step is to determine the total current and voltage in the circuit:

• The magnitude of the current in a series circuit is the same at every point in the circuit. If you know the current at any point, use that value in this equation.
• The total voltage is equal to the voltage from the power supply (battery). The total stress is not the same as the stress in one component.

Step 4. Plug these quantities into Ohm's Law

Change the formula V = IR to find resistance: R = V / I (resistance = voltage / current). Plug the quantity you found into this formula to find the total resistance.

• For example, in a series circuit a 12 V battery is connected, and the current measured is 8 Ampere. The total resistance in the whole circuit is R_T = 12 V / 8 A = 1.5 Ohms.

Method 2 of 4: Parallel Circuit

Step 1. Understand parallel circuits

A circuit is said to be parallel if it branches before reconnecting. Current flows in each branch of the circuit.

If your circuit has several resistors on the main line (before or after the branch), or there is one or more resistors on a branch, look directly at the combination circuit

Step 2. Calculate the total resistance for each branch

Since each resistor only reduces current as it passes through one branch, each resistor as a whole has little effect on the total resistance of the entire circuit. The formula for the total resistance R_T is 1RT=1R1+1R2+1R3+…1Rn{displaystyle {frac {1}{R_{T}}}={frac {1}{R_{1}}}+{frac {1}{R_{ 2}}}+{frac {1}{R_{3}}}+…{frac {1}{R_{n}}}}

, di mana R₁ adalah hambatan total pada cabang pertama, R₂ adalah hambatan total pada cabang kedua, dan seterusnya sampai cabang terakhir R .

• Misalnya, sebuah rangkaian paralel memiliki tiga cabang, dengan masing-masing hambatan 10 Ω, 2 Ω, and 1 Ω.

  Gunakan rumus 1RT=110+12+11{displaystyle {frac {1}{R_{T}}}={frac {1}{10}}+{frac {1}{2}}+{frac {1}{1}}}

  dan cari besaran R_T:

  Ubah pecahan supaya penyebutnya sama: 1RT=110+510+1010{displaystyle {frac {1}{R_{T}}}={frac {1}{10}}+{frac {5}{10}}+{frac {10}{10}}}

  1RT=1+5+1010=1610=1, 6{displaystyle {frac {1}{R_{T}}}={frac {1+5+10}{10}}={frac {16}{10}}=1, 6}

  Kalikan kedua sisi dengan R_T: 1 = 1, 6R_T

  R_T = 1 / 1, 6 = 0, 625 Ω.

Step 3. Calculate from the total current or voltage

If you don't know the size of each resistance, start with the current and voltage:

• In a parallel circuit, the voltage across one branch is equal to the total voltage across the circuit. As long as you know the magnitude of the voltage for one branch, you can start calculating. The total voltage is equal to the voltage from a power supply, such as a battery.
• In a parallel circuit, the amount of current can be different in each branch. You have to know the total current, or you won't be able to find the total resistance.

Step 4. Plug these quantities into Ohm's Law

If you know the total current and voltage for the entire circuit, you can find the total resistance using Ohm's Law: R = V/I.

• For example, a parallel circuit is given a voltage of 9 V and a total current of 3 Amperes. The total resistance is R_T = 9 V / 3 A = 3.

Step 5. Note the branch with zero resistance

If there is a branch that has no resistance at all, all current will flow through that branch. The resistance of this circuit is 0 Ohm.

In practical application, this means that a resistor is damaged or short-circuited, and large currents can damage other parts of the circuit

Method 3 of 4: Combination Circuit

Step 1. Break the circuit into series and parallel sections

A combination circuit has some components connected in series, and some in parallel (on different branches). See on the diagram which parts can be simplified into one part series or parallel. Circle each of these sections so that they are easy to work with.

• For example, suppose a circuit has a 1 resistor and a 1.5 resistor connected in series. After the second resistor, the circuit branches into two, one with a 5 resistor and the other with a 3 resistor.

  Circle the two parallel branches to separate them from the rest of the circuit.

Step 2. Find resistance for parallel sections

Use the parallel resistance formula 1RT=1R1+1R2+1R3+…1Rn{displaystyle {frac {1}{R_{T}}}={frac {1}{R_{1}}}+{frac {1} {R_{2}}}+{frac {1}{R_{3}}}+…{frac {1}{R_{n}}}}

untuk mencari hambatan total dari bagian paralel pada rangkaian.

• Rangkaian pada contoh memiliki dua cabang paralel dengan hambatan R₁ = 5 Ω dan R₂ = 3 Ω.

  1Rparalel=15+13{displaystyle {frac {1}{R_{paralel}}}={frac {1}{5}}+{frac {1}{3}}}

  1Rparalel=315+515=3+515=815{displaystyle {frac {1}{R_{paralel}}}={frac {3}{15}}+{frac {5}{15}}={frac {3+5}{15}}={frac {8}{15}}}

  Rparalel=158=1, 875{displaystyle R_{paralel}={frac {15}{8}}=1, 875}

  Ω

Step 3. Simplify the diagram

Once you find the total resistance in a parallel section, cross that section off the diagram. Think of the part as a component with a resistance equal to the quantity you have found.

In the example above, ignore the two branches and treat it like a resistor with a resistance of 1.875

Step 4. Add resistance in series

Once you change the parallel section to a single resistor, the diagram becomes as simple as a series circuit. The total resistance of a series circuit is equal to the sum of all the resistances, so add them all up to get the answer.

• The simplified diagram has one 1 resistor, one 1.5 resistor, and a section with 1.875 resistance as we calculated earlier. All of these circuits are connected in series, so RT=1+1, 5+1, 875=4, 375{displaystyle R_{T}=1+1, 5+1, 875=4, 375}

  Ω.

Step 5. Use Ohm's Law to find the unknown quantity

If you don't know the resistance of a component in the circuit, find a way to find it. If you know the voltage V or current I in the component, find its resistance using Ohm's law: R = V/I.

Method 4 of 4: Formula Using Power

Step 1. Learn the power formula

Power is the rate at which energy is used in a circuit, and at that rate energy is transferred to the circuit to light something (such as a lamp). The total power in a circuit is equal to the product of the total voltage by the total current. In equation form: P = VI.

Remember that when looking for total resistance you must know the total power of the circuit. It's not enough just to know the power that flows in one of the components

Step 2. Find resistance using power and current

If you know these two quantities, you can combine the two formulas to find resistance.

• P = VI (power = voltage x current)
• From Ohm's Law we know that V = IR.
• Substitute IR into V in the first formula: P = (IR)I = I²R.
• Change the formula to get the resistance formula: R = P / I².
• In a series circuit, the current in one component is equal to the total current. This does not apply to parallel circuits.

Step 3. Find resistance using power and voltage

If you only know power and voltage, you can use the same approach to find resistance. Always remember to use the total voltage of the entire circuit, or the voltage from the batteries installed in the circuit:

• P = VI
• Change the order of Ohm's Law in I: I = V/R.
• Substitute V / R into I for the power formula: P = V(V/R) = V²/R.
• Change the formula to get the resistance: R = V²/P.
• In a parallel circuit, the magnitude of the voltage from one branch is equal to the total voltage. This does not apply to series circuits: the voltage across one component is not equal to the total voltage.

Tips

• Power is measured in watts (W).
• Voltage is measured in volts (V).
• Current is measured in amperes (A). 1 mA = 1∗10−3{displaystyle 1*10^{-3}}

  a = 0, 001 a.

• besaran daya p yang digunakan di dalam rumus ini mengacu pada daya sesaat, atau daya pada waktu tertentu. jika rangkaian menggunakan sumber daya ac, dayanya selalu berubah. ahli kelistrikan menggunakan daya ac rata-rata saat memakai rumus p_rata-rata = vi cosθ, di mana cosθ adalah faktor daya dari rangkaian.