Resistance
(R)
is defined as the ratio of the voltage (V) across a conductor to the
current (I) flowing through it. Mathematically, therefore, R = V/I,
which is also known as Ohm's Law. The unit
of measurement for resistance is the 'ohm', Ω, which is defined as
volt/ampere (volt and ampere are the units of measurement for voltage
and current, respectively). A component fabricated to exhibit
nothing but a certain resistance (ideally) is known as a
resistor.
The higher
the resistance, the greater is the voltage required to attain a given
amount of current flow. Resistance is therefore, as its name
implies, a measure of the ability of a conductor to resist the flow of
current.
 |
|
Figure 1. Photo of Resistors |
Resistance is
an extrinsic property, i.e., its value is affected by characteristics
that are not inherent to the conductor, such as the conductor's
dimensions. The inherent characteristic of a material that defines
its ability to resist the flow of current is known as its 'resistivity',
ρ. The resistance R is related to the resistivity ρ by the equation:
R =
ρL/A,
where L is the length of the conductor and A is its cross-sectional
area.
Resistors may
be connected to each other to form new values of resistance. They may be
connected in series or in parallel, as shown in Figure 2.
 |
 |
|
Figure 2. Resistors in parallel (left) and in
series (right) |
When two or
more resistances are connected in
series,
the currents through each of them are equal. However, the
corresponding voltage developed across each of them differs in
accordance with Ohm's Law. Thus, for a given
circuit consisting of N resistors connected in series and excited by a
voltage V, I = V1/R1 = V2/R2 = ... = VN/RN, where I is the current
flowing through the circuit and Vi is the corresponding voltage
developed across every individual resistance Ri, such that V = V1
+ V2 +... + VN.
The
effective resistance of such as circuit is Reff = V/I = (V1 + V2 +
... + VN) / I = (IR1 + IR2 + ... + IRN)/I. This equation may
be simplified as follows: Reff = R1 + R2 + ... + RN.
Thus, the
effective resistance of N resistances connected in series is
just the sum of the individual resistances, i.e., Reff = R1 + R2 +
... + RN.
When two or
more resistances are connected in
parallel,
the voltages across each of them are equal. However, the
corresponding current flowing through each of them differs in accordance
with Ohm's Law. Thus, for a given circuit
consisting of N resistors connected in parallel and excited by a voltage
V, V = I1R1 = I2R2 = ... = IN/RN, where Ii is the
corresponding current flowing through every individual resistance Ri.
In such a
circuit, the current I flowing through the entire circuit is the sum of
the individual currents flowing through each corresponding resistor, or
I = I1 + I2 + ... + IN, which may be rewritten as V/Reff = V/R1 + V/R2 +
... + V/RN. This equation may be simplified as follows: 1/Reff =
1/R1 + 1/R2 + ... + 1/RN.
Thus, the
reciprocal of the
effective resistance of N resistors connected in parallel is
equal to the sum of the reciprocals of the individual resistances.
i.e.,
1/Reff = 1/R1 + 1/R2 + ... + 1/RN.
See Also:
Resistor Value Color Coding;
Ohm's Law;
Capacitance;
Self-Inductance
