Series Circuits

From our studies of series circuits in the laboratory we found that they have several important characteristics.

   Circuit Legend:

     V_T is the Total Voltage

    I_T is the total Current

   V₁, V₂, and V₃ are the voltage drops across R₁, R₂,
   and  R₃ respectively.

    I₁, I₂, and I₃ are the currents through R₁, R₂,
   and  R₃ respectively.

Series Circuits Facts:

Example:

In the circuit below, find all the unknown quantities:

Solution:

(i)  If  I₂₌ 10 A, Then  I₁ =  I₂ = I₃ = I_T = 10 A  (Current is constant in a series circuit)  

(ii) FOR R₁        V₁ = I₁  x R₁ = 10A x 1.0 Ω  = 10 V

(iii) FOR V₃    We know that V_T = V₁ + V₂ +V₃
        Therefore   100 V = 10V + 50V + V₃
                                         V₃ = 100V - 5-V - 10 V =  40V

(iv) Now we can find R ₃
                                R ₃  = V ₃ / I ₃  =  40V / 10A = 4 Ω

(v) Find  the Total Resistance R_T

1. Method #1 -----  R_T = R₁ + R₂ +  R₃   = 1.0 Ω  + 5 Ω  + 4 Ω  = 10Ω  
    
2. Method #2 ------ R_T  = V_T / I_T      (Ohm's Law)
                                                 =  100 V / 10 A  = 10 Ω
   You can see that both methods yield the same result

(vi)   Find  P₁       P₁ =  V₁ x  I₁ = 10 V x 10 A = 100 W
                                    This is the power used by R₁

(vii)  Find  P₂       P₂ =  V₂ x  I₂ = 50 V x 10 A = 500 W
                                     This is the power used by R₂

(viii)  Find  P₃      P₃ =  V₃ x  I₃ = 40 V x 10 A = 400 W
                                     This is the power used by R₃

(ix)   Find  P_T       P_T =  V_T x  I_T = 100 V x 10 A = 1 000 W
                                       This is the total power used by all three resistors together
        
          Or, Alternatively, P_T = P₁ + P₂ + P₃  = 100 W + 500 W + 400 W = 1 000 W
You can see that both methods yield the same results

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