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2.8 
suMMary
• Let a circuit contain b-elements, l-loops and n-nodes, and let it have a unique solution. Then 
the ‘circuit analysis problem’ involves solving for 2b variables – one voltage variable and one 
current variable per two-terminal element. b equations are obtained by using the element relation 
of b elements. The remaining b equations come from applying Kirchhoff’s Current Law and 
Kirchhoff’s Voltage Law. KVL and KCL equations depend only on the topology of the circuit and 
do not depend on the nature of elements.
• A node in a circuit is a junction point at which the connection leads of two or more points join together. The 
node is part of the connecting wire. Hence, according to the assumptions involved in lumped parameter 
circuit theory, there is negligible charge storage and negligible rate of change of charge storage at a node.
• Therefore, the net positive current that enters (or leaves) a node in a circuit through all the 
connecting wires connected at that node has to be zero. This is the Kirchhoff’s Current Law. 
• Kirchhoff’s Current Law can be stated in three forms as follows:
Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents leaving a node in a 
lumped parameter circuit is equal to zero on an instant-to-instant basis.
Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents entering a node in a 
lumped parameter circuit is equal to zero on an instant-to-instant basis.
Kirchhoff’s Current Law (KCL) states that the sum of currents entering a node in a lumped 
parameter circuit through some wires must be equal to the sum of currents leaving the same 
node through the remaining wires on an instant-to-instant basis.
• Kirchhoff’s Current Law is also valid for any closed surface that intersects connecting wires and 
encloses more than one node and one or more elements without intersecting any element. Such a 
closed surface is called a supernode of the circuit.
• KCL equations for any (n
-
1) nodes in a n-node circuit will form an independent set of equations. 
• A loop in a circuit is closed path traced through nodes, connecting wires and elements such that 
no node is visited more than once in one complete traversal of the closed path.
• Kirchhoff’s Voltage Law for such a loop in a circuit can be stated in three equivalent forms as follows:
Kirchhoff’s Voltage Law states that the algebraic sum of voltages in any closed path in a 
lumped parameter circuit is zero on an instant-to-instant basis. 
Kirchhoff’s Voltage Law states that the sum of ‘voltage rises’ in any closed path in a lumped 
parameter circuit is zero on an instant-to-instant basis.
Kirchhoff’s Voltage Law states that the sum of ‘voltage drops’ in any closed path in a lumped 
parameter circuit is zero on an instant-to-instant basis.
• A planar circuit is one that can be represented on a paper without crossing of connecting wires. Those 
closed loops that do not contain other loops within them in a planar circuit are called its meshes.
• The KVL equations for meshes in a planar circuit will be an independent set of equations.
• A set of two-terminal elements is said to be series-connected if a common current can flow through them.
• A set of two-terminal elements is said to be parallel-connected if they share the same node-pair. 
In this case, it is possible to make the terminal voltage variables of all such elements a common 
variable by suitable reference polarity assignment for voltage variables.
• An Operational Amplifier is a muti-stage high gain voltage-to-voltage amplifier with differential 
input and single-ended output. It is a differential amplifier and has two signal input terminals. 
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Problems 
2.35
It amplifies the difference between the voltages applied at input terminals. These two input voltages 
as well as the output voltage are referred to a common ground terminal.
• An Ideal Operational Amplifier (IOA) is a voltage-to-voltage differential amplifier with infinite 
input resistance, zero output resistance, infinite differential gain, zero common mode gain, infinite 
bandwidth, no output current and rate restrictions, no offsets and no input bias currents.
• A simple interchange of the roles of inverting input terminal and non-inverting input terminal 
of an Opamp in circuit changes the nature of feedback in the circuit and affects the function and 
operation of the circuit significantly. 
• The principle of virtual short – The input terminals of an ideal Opamp in a negative feedback 
circuit behave as if there is a short-circuit across them. The input terminals of a practical Opamp 
with large gain behave as if there is short-circuit across them provided the Opamp is in a negative 
feedback circuit and it is operating in its linear range.
• The principle of zero input current – The input terminals of an ideal Opamp do not draw any 
current from the circuit in which the Opamp is embedded. 
• These two principles can be used to analyse Opamp circuits quickly, provided the Opamp is in a 
negative feedback circuit and is in its linear range of operation.