2. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 2
Resistors
Resistance
Property which opposes the flow of current
R = V/I
Unit – Ohms (Ω)
Power P = VI = V2
/R = I2
R
Conductance
Reciprocal of resistance
Symbol: G
Unit – Siemens (S)
R
V
I
3. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 3
Problem - 1
4. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 4
Problem - 2
5. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 5
Resistivity & Temperature Coefficient
( )
( )
( )20
10
2
1
0
1001
1
1
Where
1
θα
θα
α
θα
+
+
=
+=
R
R
RR
For a homogeneous material
Where
= resistivity
a = cross sectional area of the Resistor
l = length of the Resistor
ρ
= Temperature coefficient of R at 0o
a
l
R ρ=
6. 0
R
R1
R0
R2
θ1 θ2
θ
Variation of Resistance of Copper with Temperature
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 6
Resistivity & Temperature Coefficient
Super Conductivity !
( )1001 1 θα+= RR
7. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 7
Temperature Coefficients
of Resistivity
Material Temperat
ure
Coefficien
t °C-1
@
0° C
Aluminum 0.00381
Copper 0.00428
Gold 0.0034
Tungsten 0.0045
Brass 0.001
Manganin 0.00002
Carbon (graphite) -0.00048
Germanium (pure) -0.048
Silicon (pure) -0.075
Material at 0° C
Aluminium 2.7 * 10 -8
Copper 1.59 * 10 -8
Tungsten 5.35 *10 -8
Carbon 6500 * 10 -8
Manganin 42 * 10 -8
ρ
Resistivity:
Resistivity & Temperature Coefficient
8. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 8
Problem- 3
When a potential difference of 10 V is applied to a coil of copper wire of
mean temperature 20° C, a current of 1.0 A flows in the coil. After some
time the current falls to 0.95 A yet the supply voltage remains unaltered.
Determine the mean temperature of the coil given that the temperature
coefficient of resistance of copper is 4.28 * 10-3
/°C referred to 0° C.
[33.5 o
C]
9. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 9
Resistive circuits
Resistors in series:
Resistors in parallel:
R1R2
R3
321
1111
RRRReq
++=
10. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 10
Parallel Resistive circuits
Current Division in Parallel Circuits
( )
1 2
1 21
1 1 1
2 2
2
1
1 2
1
2
1 2
I I I
R RR
I I I
R R
R
I I
R R
R
I I
R R
= +
+
= + =
=
+
=
+
