167.MET February 2022 Q.7

 With reference to adjoining circuit calculate following. 

(a) Current in each branch of the circuit

(b) Total current

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Given

V = 100 V

f = 50 Hz

R = 50 ohm

L = 0.15 H

C = 100 micro F

To find

(a) Current in each branch of the circuit

(b) Total current

Solution

The total current, IS drawn from the supply is equal to the vector sum of the resistive, inductive and capacitive current, not the mathematic sum of the three individual branch currents, as the current flowing in resistor, inductor and capacitor are not in same phase with each other; so they cannot be added arithmetically.

Apply Kirchhoff’s current law, which states that the sum of currents entering a junction or node, is equal to the sum of current leaving that node we get,

Let V is the supply voltage.
IS is the total source current.
IR is the current flowing through the resistor.
IC is the current flowing through the capacitor.
IL is the current flowing through the inductor.

Inductive reactance XL = 2πfL

                                      = 2 x 3.14 x 50 x 0.15

                                      = 47.1 ohm

Capacitive reactance Xc = 1 / (2πfc)

                                        = 1 / (2 x 3.14 x 50 x 0.001)

                                        = 3.18 ohm

a) Current through resistor IR = V/R

                                               = 100/50

                                               = 2 A

    Current through Inductor IL = V/XL

                                                = 100/47.1

                                                = 2.12 A

    Current through capacitor Ic = V/Xc

                                                  = 100/3.18

                                                  = 31.44 A

b)  Total current I_S = √ [I_R² + (I_L - I_C)²]

                                  = √ [2² + (2.12 - 31.44)²]

                              = 29.38 A

              Ff

2πfL=2×3.14×100×0.02