Simplifier Formulas for Series and Parallel Circuits Resistance Calculations

Combining Resistors

• Resistors are in either fixed or variable range. It would be impracticable for manufacturers to build resistors in that form, they don’t exist at all. 
• A 25k resistor, for instance, may be impossible to locate, whereas 22k resistors are widespread and are available almost anywhere.

Series Resistance Circuit

When two resistors are connected in series, the current is first limited or restricted by the first resistor and then further limited or restricted by the second resistor, increasing the effect of the series connection. 

Equivalent Series Resistance

The total resistor value in a series circuit connection is equal to R, R_series, or R_eq or R _effective.

R = R₁+R₂+ R₃

Problem 1

Determine the value of equivalent resistance in the following circuit.

Req = 1200 + 680 + 470 Ω = 2350 Ω

Current Flow & Voltage Drops across the Series Elements

• There is only one direction for the current, I, to move. 
• As a result, each resistor is experiencing the same amount of current, I. 
• Each resistor is experiencing the same amount of current, I. 
• The potential difference, V, is directly proportional to resistance R.

I = I₁= I₂ = I₃

V= V₁+V₂

The V_out in a given circuit is calculated as

Simplified formula for same value resistance in series (R₁ = R₂ = R₃)

• The total or equivalent resistance, R_T, is equal to double the value of one resistor if two identical resistances or impedances are connected in series. 
• That is equal to 2R, 3R, etc., for three identical resistors connected in series. 

Finding unknown resistor in circuit 

• When total resistance is known, the unknown resistance value in circuit can be found by subtracting known resistor value from equivalent resistor of the circuit. ( R_x= R_eq – R₁ )
• When applied voltage and current flow in circuit is known then Req is found by V/I. Same procedure mentioned above is followed to determine unknown resistance

Problem 2

If one of the resistors has a resistance of 2Ω. Determine the value of the other resistor when total resistance is 7Ω

R_x= R_eq – R₁= 7 – 2 = 5 Ω

R_x= R₂ = 5 Ω

Parallel Resistance Circuit

• When a resistor is connected in parallel, two paths for current flow are created. 
• Parallelism has the effect of lowering overall resistance. 
• Equivalent Parallel Resistance

The equivalent resistance.

The corresponding / effective resistance for 2 resistors in parallel

When paralleling more than two or three resistors 

The equivalent /effective resistance becomes 

Problem 3

Two resistors with resistances of 3 and 6 are linked in parallel, which is a problem. Identify the overall resistance.

Current Flow & Voltage Drops across the Parallel Elements

• There are various ways for the current to flow. 
• The aggregate of the currents in the various pathways is what we refer to as the current, both leaving and returning to the source.

• Given that the two bulbs share the same two points, the potential difference between them is the same.
• As a result V= V₁= V₂

Equivalent resistance for more than three resistor in parallel

Simplified formula for same value resistance in parallel (R₁ = R₂ = R₃)

The total or equivalent resistance, R_T, is equal to half the value of one resistor if the two parallel resistances or impedances are equal and of the same value. That is equivalent to R/2, R/3, etc., for three parallel resistors of identical value.

Problem 4

Determine the equivalent resistor in following circuit.

Finding unknown resistance in parallel combination 

Problem 5

What resistance value needs to be added in parallel to an 12 ohm resistor in circuit to produce a total resistance of 3 ohms?

R₁ = 12 ohm & R_T= 3 ohm 

From above formula R₂ = (12×3)/ (12 – 3) = 4 ohms

Comparison of Series & Parallel Combination