Series Circuits

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

   Circuit Legend:

     VT is the Total Voltage

    IT 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:

Voltage

The sum of all the voltage drops adds up to the total (source) voltage

VT = V1 + V2 +V3

Current

The current is always the same

IT  = I1 = I2 = I3

Resistance

The Total resistance RT  can be calculated in two possible ways:

  1. RT = R1 + R2 +  R3  
     
  2. RT  = VT / IT    (Ohm's Law)
Power

The Total Power PT  can be calculated in two possible ways:

  1. PT = P1 + P2 + P3  
     
  2. PT  = VT  IT   

 

Example:

In the circuit below, find all the unknown quantities:

GIVENFINDFIND
 VTotal  = VT = 100 VIT= ?RT= ?
V2 = 50 VV1 =R 3= ?
R2 = 5.0 ΩV3 =P1 = ?
R1 = 1.0 ΩI1 = ?P2 = ?
I2= 10 AI3 = ?PT = ?

Solution:

(i)  If  I2= 10 A, Then  I1 =  I2 = I3 = IT = 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 VT = 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 RT

  1. Method #1 -----  RT = R1 + R2 +  R3   = 1.0 Ω  + 5 Ω  + 4 Ω  = 10Ω  
     
  2. Method #2 ------ RT  = VT / IT      (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  PT       PT =  VT x  IT = 100 V x 10 A = 1 000 W
                                       This is the total power used by all three resistors together
        
          Or, Alternatively, PT = P1 + P2 + P3  = 100 W + 500 W + 400 W = 1 000 W
You can see that both methods yield the same results
 

  Back to the Top

Try some Exercises

  Home