Behavior and properties of DC circuit.

Power sources basically two types AC and DC discussed previously .If we applied DC voltage in a circuit called DC circuit.

DC CIRCUIT

                               DC circuit is three types 1. Series 2. Parallel 3. Combination of series and parallel.

1. In a series circuit flow of electrons moved to one path towards battery positive terminal to negative terminal. In figure 9 V DC voltage source applied flow of electrons 1-2-3-4 through all the resistances. In a Series the equivalent value of resistance R=R1+R2+R3 i.e. Total value of resistances(R)=3+10+5= 18 kohm. According to ohms law the value of current in this circuit I=V/R means I=9/18=0.5 Amps. The value of voltage different at different resistance at R1 voltage is V1= IxR1=0.5 X 3 =1.5 V DC similarly at R2 5 V DC and R3 2.5 V DC.We can say in series circuit the voltage is different at different resistance but sum is equal to source voltage.

DC series circuit

• Total voltage=v1+v2+v3...Voltage different at different resistance.
• Total current= I1=I2=I3…Current same through the circuit.
• Total Resistance=R1+R2+R3...Resistance added.
• Total Capacitance= 1/c1+1/c2+1/c3...When capacitor connected in series DC circuit.
•  Total Inductance = L1+L2+L3...When inductance connected in series DC circuit.
• Voltage Diversion V1=I*R1,V2=I*R2 ...and so on
• Current Diversion I1=V1/R1,I2=V2/R2...are same.

 I    2.In parallel circuit the flow of electrons is different in different branches. In this figure below there are three resistancesR1,R2 and R3 arrangement in parallel branches 2-7,3-6 and 4-5 the flow current is different in every branch but the value of voltage is same in throughout the circuit i.e. 9 VDC. The value of total resistance in the circuit 1/R=1/R1+1/R2+1/R3 means R=R1*R2*R3/R1+R2+R3 in this circuit R=10*2*1/10+2+1=20/13, R= 1.54kohm. Total current I(R1)=V/R1,9/10=0.9 A(branch 2-7) similarly I(R2)=4.5 A,( branch 3-6) I(R3)=9 A( branch 4-5)i.e.  I(T)=I(R1)+I (R2)+ I(R3)=14.4 A. 

DC Parallel circuit

• voltage=v1=v2=v3...Voltage same through the same circuit.
• Total current= I1+I2+I3…Current is the sum of all branches.
• Total Resistance=1/R1+1/R2+1/R3…Division of Resistance added.
• Total Capacitance= c1+c2+c3…When capacitor connected in parallel DC circuit.
• Total Inductance =1/ L1+1/L2+1/L3 ...When inductance connected in series DC circuit.
•  Voltage Diversion V1=Total voltage *R1/(R1+R2+R3)…and so on
• Current Diversion I1=Total current*(R2+R3+..)/(R1+R2+R3+… are same. 

 3. In Combination series parallel circuit resistances are connected in the combination of series and parallel shown in below image R1,R2and R3, R4 in parallel means R(12)= R1*R2/R1+R2 and R(34)=R3*R4/R3+R4areinseriesR(12)=100*250/100+250=71.4ohms,R(34)=350*200/350+200=127.27 ohms. Here R (12) and R (34) in series i.e. total value of in this circuit R (Total) = R (12) + R (34) =198.67 ohms. Then the Value of current is 24/198.67=0.12A and voltages at are different at R (12), R (34) we can calculate as similarly to series circuit.

combination of series and parallel

DC circuit rules:

1. I=V/R (Ohms law)

2. P=V.I=sqr.of  IR= sqr.of V/R (Joule law)

3. ƩVi=0 at a current loop sum of voltage drop is Zero (Kirchhoff’s voltage law).

4. ƩIi=0 at a node sum of currents values is Zero (Kirchhoff’s current law).

5. C=Q/V value of capacitance= charge /voltage.

6. Energy stored in capacitor = C*sqr.of V/2

7. Energy stored in inductor = L* sqr. of I/2