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What happens to the total current in a parallel circuit when an additional branch is connected across the source?
Increases
Decreases
Stays constant
Becomes zero
Increases
In a parallel circuit, connecting an additional branch provides a new path for the current to flow. Since the voltage across all branches remains constant (equal to the source voltage), adding a parallel path reduces the total equivalent resistance of the circuit, leading to an increase in the total current drawn from the source.
In a parallel circuit, connecting an additional branch provides a new path for the current to flow. Since the voltage across all branches remains constant (equal to the source voltage), adding a parallel path reduces the total equivalent resistance of the circuit, leading to an increase in the total current drawn from the source.
ItotalтАЛ=тИСi=1nтАЛIiтАЛ=V├ЧтИСi=1nтАЛRiтАЛ1тАЛ тАФ Total current in a parallel network
ReqтАЛ=тИСi=1nтАЛRiтАЛ1тАЛ1тАЛ тАФ Equivalent resistance of parallel branches
According to Ohm's Law, total current ItotalтАЛ is determined by ItotalтАЛ=ReqтАЛVтАЛ. In a parallel circuit, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual branch resistances, expressed as ReqтАЛ1тАЛ=R1тАЛ1тАЛ+R2тАЛ1тАЛ+...+RnтАЛ1тАЛ. When a new branch RnewтАЛ is added, ReqтАЛ1тАЛ increases, which forces ReqтАЛ to decrease. Consequently, for a constant source voltage V, the total current ItotalтАЛ must increase to satisfy Kirchhoff's Current Law at the source nodes.
Voltage remains constant across all parallel branches.
Total circuit conductance increases with each additional branch.
The source experiences a higher load as total current increases.
Total power consumption increases because P=V├ЧItotalтАЛ.
Independent operation of individual loads.
Constant voltage supply to all branches.
Risk of overloading the source as more branches are added.
Requires high current capacity source for many branches.
Domestic wiring systems.
Distribution networks in power systems.
This behavior is why adding too many high-power appliances in a home (parallel circuit) can trip a circuit breaker due to excessive total current.
Option B is incorrect because adding a branch adds conductance, it never reduces total current. Option C is incorrect because total current depends on the aggregate impedance, which changes. Option D is incorrect as the current would only be zero if the source were disconnected or the circuit opened entirely.
A is correct тАФ The total current increases because the equivalent resistance of the circuit decreases while the source voltage remains constant.
Remember that in parallel circuits, adding components always increases total current, whereas in series circuits, adding components always increases total resistance and decreases current.