Resistance Capacitance and Inductance in series and parallel

Resistance Capacitance and Inductance in series and parallel

Resistance in series

When resistances are connected in series the current flowing through all resistance is same  suppose current is I amp
The voltage drop in R1 is    V1 = IR1
The voltage drop in R2 is    V2 = IR2
The voltage drop in R3 is    V3 = IR3

The total voltage  in circuit V = IR
Total voltage V = V1 ÷ V2 ÷ V3
Or  IR = IR1 ÷ IR2÷ IR3
Cancelling out I from both side then we get

R = R1 ÷ R2 ÷ R3

For example if two resistance of 5 ohms and 8 ohms are in series there equivalent resistance is equal to 5 ÷ 8 = 13 ohms.

Resistance in parallel

As shown in circuit three resistances R1, R2 and R3 are connected in parallel the equivalent resistance can be found as below.

Voltage across each resistance is same as V volt

Total current I = I1 ÷ I2 ÷ I3
By ohms law  I1 = V/R1,     I2 = V/R2    and     I3 = V/R3
Summing up all three current total current
I = I1 + I2 + I3
Or
V/Req  = V/R1 ÷ V/R2÷ V/R3

Cancelling  V in both side we get

1/Req = 1/R1 ÷ 1/R2 ÷ 1/R3

For example two resistance of 4 and 12 ohms are connected in parallel there equivalent resistance is

1/R = 1/4 ÷ 1/12 = (3÷1)/12 = 4/12 = 1/3 ohms

There fore R  = 3 ohms

Capacitance in series

Similarly in capacitance if three capacitance are connected in series as shown in figure the equivalent capacitance  can be find as below

If the capacitors are connected in series the charge on each capacitor is equal to total charge Q.
voltage across each  capacitors is given by

V1 = Q/C1,   V2 = Q/C2    and   V3 = Q/C3

Total voltage V = Q/Ceq

Total voltage V = V1 + V2 + V3

Or   Q/Ceq = Q/C1 + Q/C2 + Q/C3

Cancelling  Q in both side we get

Or     1/Ceq = 1/C1  ÷  1/C2  ÷ 1/C3

Capacitance in parallel

If three capacitance are connected in parallel as shown in figure the equivalent capacitance is given by

In Parallel voltage across each capacitor is equal to applied voltage V
Charge on capacitor is

Q1 = VC1,   Q2  = VC2     and   Q3 = VC3
Total charge Q = Q1 + Q2  + Q3   eq --(1)
Putting value of  Q1,  Q2,  and Q3  in eq (1) we get
VC = VC1 + VC2 + VC3

Cancelling out V on both side we get

Ceq = C1 ÷ C2 ÷ C3

Inductance in Series

For inductance if three inductance are  connected in series (not mutually linked) the equivalent inductance is equals to

L = L1 ÷ L2 ÷ L3

Inductance in Parallel

If three inductance are connected in parallel the equivalent inductance is given by

1/L  = 1/L1 ÷  1/L2  ÷ 1/L3

Simple ac circuit

If a resistance is connected to dc supply of voltage V the current I  through resistance R is given by ohm's law

I= V/R amp

But in case of  capacitance and inductance the term capacitive reactance and inductive reactance is used.

Capacitive reactance is equals to 1/2πfC.

Inductive reactance is equals to 2πfL.

Where f is the frequency of ac supply. These formulas are used for ac supply  of any frequency. For dc voltage calculations are done differently.

If a resistance, capacitance and inductance are connected in series then their effective resistance to flow  of  current is known as Impedance Z of the circuit. Z is given by formula

Now for ac circuit if voltage is Vrms, Impedance is Z then current is given by

Irms = Vrms/Z

The term RMS is generally not written but  it  is always there. All readings given by meters are RMS values.