Resistors in Series

 Series Configuration

When two or more resistors are connected in series. It creates a single path for the flow of electric current.

• The current through each of the resistors remains the same.
  
  
• The potential difference is the sum of the individual potential difference across each resistor.
  
  
• Equivalent resistance of the circuit is the sum of individual resistances.

OHM’s law states that - Electric current flowing through an ideal conductor is directly proportional to the Potential Difference or Voltage across the two ends of the conductor.

⸫ V_AB = I x R₁, V_CD = I x R₂ and V_EF = I x R₃   ------------- (i)

       V = V_AB + V_CD + V_EF                                   ------------- (ii)

Let’s assume that R₁, R₂, R₃ is replaced by a Single Resistance R_s. The question is what will be the value of R_s? Then from ohm’s law –

V = I x R_s                                                                                ------------- (iii)

From (ii) & (iii), we have

I x R_s   = V_AB + V_CD + V_EF                                 ------------- (iv)

Using (i) in (iv), we get

I x R_s = I x R₁ + I x R₂ + I x R₃

R_s = R₁ + R₂ + R₃

The Equivalent resistance of the circuit in series combination is the sum of individual resistances.

Disadvantages of Series arrangement of resistors:

• Two different electrical appliances, having different current requirements, cannot be connected in series as the current is constant (same) in a series circuit.
• If one of the components fails in a series circuit, the circuit gets broken and none of the other components get the current.
• Two electrical devices rated to work on same supply voltage cannot be connected in series as the applied voltage gets distributed across each resistors combination..

Conclusions:

In Series combination, the equivalent resistance is given by -

Rs = R1 + R2 + R3 + R4 + … + Rn

If given R1 = R2 = R3 = … = Rn = R, i.e. all Resistances are equal, then Rs = n x R Ω

The applied voltage V also get equally distributed across each Resistors V1 = V2 = V3 = Vn = V /n Volt.

Solved Numerical:

There are three resistors joined in series in a system having resistance equal to 10 Ω, 20 Ω and 30 Ω respectively. If the potential difference of the circuit is 240 V, find the total resistance and current through the circuit.

Solution: Given, R1 = 10 Ω, R2 = 20 Ω, R3 = 30 Ω and V = 240 V

To find Total resistance (R) =?

Current through the circuit (I) =?

Total resistance in series (R) = Sum of resistance of all resistors

Or, R = 10Ω + 20Ω + 30Ω = 60Ω

We know that electric current I = V /R {From ohm’s law, V = I x R

Or, I = 240 V ÷ 60 Ω

= 4 A

Current through the circuit = 4 A