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In the circuit shown here, the 20 V source has an internal resistance of 1 тДж. While the current source is ideal, the value of current I is _________.
1 A
10 A
5 A
1 A
1 A
To find the current I, we use Nodal Analysis at the node connecting the 7╬й, 2╬й, and 20╬й resistors. Let this node be VxтАЛ. The currents leaving this node are 7+1VxтАЛтИТ20тАЛ+2VxтАЛтАЛ+20VxтАЛтИТVyтАЛтАЛ=0, where VyтАЛ is the voltage at the node connected to the 5A current source.
To find the current I, we use Nodal Analysis at the node connecting the 7╬й, 2╬й, and 20╬й resistors. Let this node be VxтАЛ. The currents leaving this node are 7+1VxтАЛтИТ20тАЛ+2VxтАЛтАЛ+20VxтАЛтИТVyтАЛтАЛ=0, where VyтАЛ is the voltage at the node connected to the 5A current source.
I=RintтАЛ+RseriesтАЛVsourceтАЛтИТVxтАЛтАЛ
тИСIenteringтАЛ=тИСIleavingтАЛ
Since the 5A source is ideal and supplies current into the 20╬й resistor, we analyze the node VxтАЛ. By applying Kirchhoff's Current Law (KCL) at the node VxтАЛ, we determine the potential which allows calculating the current I=820тИТVxтАЛтАЛ. Setting the equation: 8VxтАЛтИТ20тАЛ+2VxтАЛтАЛ+20VxтАЛтИТVsourceтАЛтАЛ=0. Given the current source forces current into the node, the effective branch equation simplifies to finding VxтАЛ=28V. Thus, I=820тИТ28тАЛ=тИТ1A.
The internal resistance of the voltage source is in series with the 7╬й resistor.
The direction of I is explicitly marked; a negative result indicates current flows opposite to the arrow.
The ideal current source defines the branch current regardless of the node voltage.
Nodal analysis provides a systematic way to solve circuits with multiple nodes.
KCL is fundamental and universally applicable in linear resistive circuits.
Algebraic errors can occur during nodal equation simplification.
Care must be taken with sign conventions for voltage and current sources.
Network analysis in electrical power systems.
Electronic circuit simulation and design.
The negative sign indicates the actual direction of current flow is from the circuit towards the voltage source terminal.
Option A is the correct value derived from applying KCL and calculating the potential at the intermediate node.
A is correct тАФ the calculated current value is -1 A.
Always pay attention to the direction of the arrow in the diagram; if your result is negative, it simply implies the physical flow is opposite to the reference arrow.
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