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In a parallel circuit, if a resistor R is added in parallel to the existing network, the total equivalent resistance of the circuit will _____.
Increase
Decrease
Remain the same
Double
Decrease
In a parallel circuit, adding an additional resistor provides an extra path for the current to flow. Since the total conductance of the circuit increases, the total equivalent resistance must decrease.
In a parallel circuit, adding an additional resistor provides an extra path for the current to flow. Since the total conductance of the circuit increases, the total equivalent resistance must decrease.
ReqтАЛ1тАЛ=R1тАЛ1тАЛ+R2тАЛ1тАЛ+тЛп+RnтАЛ1тАЛ тАФ Reciprocal relationship for parallel resistors
GtotalтАЛ=G1тАЛ+G2тАЛ+тЛп+GnтАЛ тАФ Conductance additive property
When resistors are connected in parallel, the reciprocal of the total equivalent resistance is equal to the sum of the reciprocals of the individual resistances. Because each additional parallel branch increases the total branch current for a constant voltage, the effective opposition to the flow of current (resistance) is reduced.
The equivalent resistance of a parallel circuit is always less than the smallest individual resistance value in the network.
As more resistors are added in parallel, the total equivalent resistance approaches zero.
Voltage remains constant across all branches in a parallel circuit.
Total current increases as more branches are added, provided the supply voltage is constant.
Independent operation of circuit branches
Constant voltage across all components
Increasing total current can cause overheating in supply lines
Complex calculation compared to series circuits
Household electrical wiring
Power distribution systems
If R1тАЛ=10╬й and we add R2тАЛ=10╬й in parallel, ReqтАЛ=5╬й, which is a decrease.
Option A is incorrect because adding resistors in parallel decreases the opposition to current. Option C is incorrect as the circuit configuration changes the node connectivity. Option D is incorrect as resistance does not double; it would only halve if an identical resistor was added in parallel.
B is correct тАФ Adding a resistor in parallel provides an additional path for current, which inherently reduces the total equivalent resistance of the circuit.
Remember the shortcut: In parallel, adding any finite resistor will ALWAYS decrease the total resistance, whereas in series, adding any resistor will ALWAYS increase it.