Electrical Science Essay Example | Topics and Well Written Essays - 1000 words

Electrical Science - Essay Example From the current divider rule, the current flowing in a circuit divides itself according to the ratio of the resistance. For a two resistor circuit comprised of resistors R1 and R2 the current through R2 is given by; .. 16V-9I1+9I3-12I3=0 16-9I1-3I3=0 Loop 2 I312- {(I3- I2)5}-(I2 8)=0 12I3-5I3+5I2-8I2= 0 7I3-3I2= 0 Loop 3 {(I1-I3) 9}+ {(I3- I2) 5}-{(I1-I2) 6}=0 9I1-9I3+5I3-5I2-6I1+6I2=0 3I1- 4I3 + I2=0 Solving the three equations 16-9I1-3I3=0 (i) 7I3-3I2= 0 (ii) 3I1- 4I3 + I2=0 (iii) Solving the simultaneous equations From equation (ii) 7I3=3I2 (iv) Substituting equation (iv) to equation (iii) we get; 3I1- 4I3 + =0 3I1-1.67I3=0 (v) Solving equation 1 and (v) 16-9I1-3I3=0 3I3+9I1= 16 (vi) 3I1-1.67I3=0 (vii) Multiplying equation (Vii) by 3 we get 9I1-5I3=0 9I1+3I3=16 Subtracting the two equations to eliminate I1 we get -8I3=-16 I3= 2 Solving for I1 we get 9I1 +6=16 I1= Solving for I2 we get = Therefore the current through the 5 ohm resistor is given by IR2= I3- I2 IR2= 2-4.67 = -2.67 Meaning that the current flows in the opposite direction as shown in the figure below IR2= 2-4.67 = -2.67 QUESTION 3 Question 3.1 Theory For an AC circuit connected in series as shown below The impendence Z is given by: Z= R+ j X Z is the impedance R is the resistance X is the reactance The reactance of a circuit comprises of the capacitive reactance and the inductive reactance and is given by X=XL-XC Where X is the reactance XL is the inductive reactance given by XC is the capacitive reactance CalculationsCapacitive reactance= = = 15.92 Inductive reactance = = 47.1 H The magnitude of impedance = Z= 31.75 Question 3.1 b Theory For a RLC ac circuit with the XL being greater than XC , the current leads the voltage and the phasor diagram is as shown below; The phase angle is given by; The power factor for an ac circuit is given by Power factor = The power of a single phase circuit is given by