Resistance in Series

When some conductors having resistances R1,R2 and R3etc. are joined end-on-end as in Fig.
1.12, they are said to be connected in series. It can be proved that the equivalent resistance or total.
resistance between points A and D is equal to the sum of the three individual resistances. Being a
series circuit, it should be remembered that (i) current is the same through all the three conductors
(ii) but voltage drop across each is different due to its different resistance and is given by Ohm's Law
and (iii) sum of the three voltage drops is equal to the voltage applied across the three conductors.
There is a progressive fall in potential as we go from point A to D as shown
Also -I = -+1-+- I I
G G. G2 GJ
As seenfrom above, the main characteristics of a series circuit are :
I. samecurrent flows through all parts of the circuit.
2. different resistors have their individual voltage drops.
3. voltage drops are additive.
4. applied voltage equals the sum of different voltage drops.
5. resistancesare additive.
6. powers are additive.
Fig. 1.13
17
D
-Ohm's Law
1.15. Voltage Divider Rule
Since in a series circuit, same current flows through each of the
given resistors, voltage drop varies directly with its resistance. In Fig.
1.14 is shown a 24- V battery connected across a series combination
of three resistors.
Total resistance R = R I + R2 + RJ = 12 Q
According to Voltage Divider Rule, various voltage drops are :
R 2
VI = V. --R-1= 24x -12 = 4 V
R2 4
V2 = V. - = 24 x _2
= 8V
R 1
V RJ 6 J = V.- =24x-=12 V
R 12
1.16. Resistances in Parallel
Three resistances,asjoined in Fig. 1.15aresaid to be connected
in parallel. In this case (i) p.d. across all resistancesis the same
(il) current in each resistor is different and is given by Ohm's Law
and(iii) the total current i.. the sum of the three separatecurrents.
V V V
I - 1+1 +1 --+-+-
- I 2 J- R R R . I 2 3
, = ~ where V is the applied voltage.
R = equivalent resistance of the parallel combination.
~ _ -Y.+ y +-Y. or 1- = -1-+ -.l +-.L
R - RI R2 RJ R RI R2 RJ
G = GI + G2+ G]
Fig. 1.15
Now,
..
Also
R
.
12 R
.
IJ R,J
I I
V
R2
24V
RJ
-
Fig. 1.14
II RI
A
2 VI
B
4 V2
C
6 VJ
DThe main characteristics of a parallel circuit are :
I. same voltage acts across all parts of the circuit
2. different resistors have their individual current.
3. branch currents are additive.
4. conductances are additive.
5. powers are additive.