Circuits 1
Module 2: Voltage and Current Laws
IDEAL SOURCES:
A. Ideal Voltage Source
- is a two terminal device whose voltage is constant regardless of the current
through it [1].
Ideal Voltage Source Practical Voltage Source
Ideal Voltage Source has zero internal resistance is zero [2] and do not exist in
practice [3]. Terminal voltage is equal to the voltage source, Vab = Vs
Practical Voltage Source has internal resistance and represented by r or rs [1].
The internal resistance is basically small value compare with the load resistance, RL.
Terminal voltage [2], Vab = Vs – Irs = IR
B. Ideal Current Source
- is a two terminal device whose current is a constant regardless of the voltage
across it [1].
Ideal Current Source Practical Current Source
Ideal current source is a mathematical model and has infinite output
impedance (internal resistance) [3],[4]. While, practical current source has very large
output impedance compare with the load resistance connected to it (rs >> RL) [1].
COMBINATION of SOURCES:
A. Series Voltage Source
Two or more elements are in series if they are connected one after another.
The equivalent voltage of two or more voltage sources in series is the sum of the
individual voltages taking into account their polarities [1], [5].
𝑉 = 𝑉 + 𝑉 +. . +𝑉
, B. Parallel Current Sources
Two or more elements are in parallel if they are connected to the two
same junction. The equivalent current of two or more current sources in parallel
is the sum of the individual currents [2], [5].
𝐼 = 𝐼 + 𝐼 +. . +𝐼
Note:
Ideal voltage sources should not be paralleled, unless they have the same
source voltage and same polarity. Similarly ideal current sources should not be
connected in series unless they have the same source current and in the same
direction [3], [6], [7]. Two generators cannot be connected in parallel unless their
voltages are exactly identical otherwise, this results in a short circuit and generators
get damaged [6].
SERIES RESISTORS
Two or more elements are in series if they are joined end-on-end [8] and as a
result carry the same current [1], [9]. A series circuit has only one current path [10].
, Characteristic of series circuit [8], [11]:
A. The current through all resistors is same which are equal to the total circuit
current. Same current flows through all parts of the circuit.
It = i = i1 = i2 = … = in
B. The equivalent resistance of any number of resistors connected in series is the
sum of the individual resistances.
Resistances are additive: 𝑅 = 𝑅 = 𝑅 + 𝑅 + ⋯+𝑅 = ∑ 𝑅
𝐺= then, = = + + ⋯+ =∑
C. Voltage drop across each is different due to its different resistance and is given
by Ohm’s Law. The larger the resistance, the larger the voltage drop.
D. The total voltage of the circuit is equal to the sum of individual voltage drop in
each resistor.
Voltage drops are additive: 𝑣 = 𝑣 = 𝑣 + 𝑣 + ⋯+𝑣 = ∑ 𝑣 =𝐼𝑅
E. Powers are additive: 𝑃 = 𝑃 = 𝑃 = 𝑃 = 𝑝 + 𝑝 + ⋯ + 𝑝 = ∑ 𝑝 =𝐼 𝑅 =
PARALLEL RESISTORS
Two or more elements are in parallel if they are connected to the same two
nodes [11] and consequently have the same voltage across them [9]. A parallel circuit
has more than one current path [10].
A node is the point of connection between two or more branches [11], [12]. If a short
circuit (a connecting wire) connects two nodes, the two nodes constitute a single node.
While, a branch is a conducting path between two nodes in a circuit containing one or
more circuit elements [13], [14], [15].
Characteristics of parallel circuit [11], [8]:
A. The same voltage v is impressed across all resistors which are equal to the total
impressed emf. Same voltage acts across all parts of the circuit.
Vt = v = vab = v1 = v2 = … = vn
B. Current in each resistor is different due to its different resistance and is given by
Ohm’s Law. Larger current flows through the smaller resistance.
C. The total current for the complete circuit is equal to the sum of the individual
branch current.
Branch currents are additive: 𝐼 = 𝑖 = 𝑖 + 𝑖 + ⋯ + 𝑖 = ∑ 𝑖 =
Module 2: Voltage and Current Laws
IDEAL SOURCES:
A. Ideal Voltage Source
- is a two terminal device whose voltage is constant regardless of the current
through it [1].
Ideal Voltage Source Practical Voltage Source
Ideal Voltage Source has zero internal resistance is zero [2] and do not exist in
practice [3]. Terminal voltage is equal to the voltage source, Vab = Vs
Practical Voltage Source has internal resistance and represented by r or rs [1].
The internal resistance is basically small value compare with the load resistance, RL.
Terminal voltage [2], Vab = Vs – Irs = IR
B. Ideal Current Source
- is a two terminal device whose current is a constant regardless of the voltage
across it [1].
Ideal Current Source Practical Current Source
Ideal current source is a mathematical model and has infinite output
impedance (internal resistance) [3],[4]. While, practical current source has very large
output impedance compare with the load resistance connected to it (rs >> RL) [1].
COMBINATION of SOURCES:
A. Series Voltage Source
Two or more elements are in series if they are connected one after another.
The equivalent voltage of two or more voltage sources in series is the sum of the
individual voltages taking into account their polarities [1], [5].
𝑉 = 𝑉 + 𝑉 +. . +𝑉
, B. Parallel Current Sources
Two or more elements are in parallel if they are connected to the two
same junction. The equivalent current of two or more current sources in parallel
is the sum of the individual currents [2], [5].
𝐼 = 𝐼 + 𝐼 +. . +𝐼
Note:
Ideal voltage sources should not be paralleled, unless they have the same
source voltage and same polarity. Similarly ideal current sources should not be
connected in series unless they have the same source current and in the same
direction [3], [6], [7]. Two generators cannot be connected in parallel unless their
voltages are exactly identical otherwise, this results in a short circuit and generators
get damaged [6].
SERIES RESISTORS
Two or more elements are in series if they are joined end-on-end [8] and as a
result carry the same current [1], [9]. A series circuit has only one current path [10].
, Characteristic of series circuit [8], [11]:
A. The current through all resistors is same which are equal to the total circuit
current. Same current flows through all parts of the circuit.
It = i = i1 = i2 = … = in
B. The equivalent resistance of any number of resistors connected in series is the
sum of the individual resistances.
Resistances are additive: 𝑅 = 𝑅 = 𝑅 + 𝑅 + ⋯+𝑅 = ∑ 𝑅
𝐺= then, = = + + ⋯+ =∑
C. Voltage drop across each is different due to its different resistance and is given
by Ohm’s Law. The larger the resistance, the larger the voltage drop.
D. The total voltage of the circuit is equal to the sum of individual voltage drop in
each resistor.
Voltage drops are additive: 𝑣 = 𝑣 = 𝑣 + 𝑣 + ⋯+𝑣 = ∑ 𝑣 =𝐼𝑅
E. Powers are additive: 𝑃 = 𝑃 = 𝑃 = 𝑃 = 𝑝 + 𝑝 + ⋯ + 𝑝 = ∑ 𝑝 =𝐼 𝑅 =
PARALLEL RESISTORS
Two or more elements are in parallel if they are connected to the same two
nodes [11] and consequently have the same voltage across them [9]. A parallel circuit
has more than one current path [10].
A node is the point of connection between two or more branches [11], [12]. If a short
circuit (a connecting wire) connects two nodes, the two nodes constitute a single node.
While, a branch is a conducting path between two nodes in a circuit containing one or
more circuit elements [13], [14], [15].
Characteristics of parallel circuit [11], [8]:
A. The same voltage v is impressed across all resistors which are equal to the total
impressed emf. Same voltage acts across all parts of the circuit.
Vt = v = vab = v1 = v2 = … = vn
B. Current in each resistor is different due to its different resistance and is given by
Ohm’s Law. Larger current flows through the smaller resistance.
C. The total current for the complete circuit is equal to the sum of the individual
branch current.
Branch currents are additive: 𝐼 = 𝑖 = 𝑖 + 𝑖 + ⋯ + 𝑖 = ∑ 𝑖 =
