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In a parallel circuit with three resistors R1, R2, and R3, if R2 becomes an open circuit, the total equivalent resistance of the circuit:
Decreases
Increases
Remains unchanged
Becomes zero
Increases
In a parallel circuit, the total equivalent resistance decreases when more branches are added. If a resistor becomes an open circuit, that branch is removed, effectively reducing the number of parallel paths, which causes the total equivalent resistance to increase.
In a parallel circuit, the total equivalent resistance decreases when more branches are added. If a resistor becomes an open circuit, that branch is removed, effectively reducing the number of parallel paths, which causes the total equivalent resistance to increase.
ReqтАЛ1тАЛ=R1тАЛ1тАЛ+R2тАЛ1тАЛ+R3тАЛ1тАЛ тАФ Equivalent resistance for three parallel resistors
ReqтАЛ=R1тАЛ+R3тАЛR1тАЛR3тАЛтАЛ тАФ Equivalent resistance after R2тАЛ becomes an open circuit
The equivalent resistance ReqтАЛ of resistors in parallel is given by the reciprocal sum. When a resistor is disconnected (open circuit), its effective resistance becomes infinite, removing its contribution to the parallel combination. Since fewer parallel paths are available for current to flow, the total resistance of the network must increase compared to the initial state.
Adding a resistor in parallel always decreases the total equivalent resistance.
Removing a resistor (open circuiting) from a parallel combination always increases the total equivalent resistance.
In a parallel circuit, ReqтАЛ is always smaller than the smallest individual resistor value.
Parallel configurations allow independent operation of circuit branches.
Constant voltage across all parallel components.
Higher complexity in wiring compared to series circuits.
Total circuit power consumption is higher as more branches are added.
Domestic lighting and appliance wiring.
Power distribution networks.
If R2тАЛ is removed, the circuit effectively becomes a two-resistor parallel circuit.
Option A is incorrect because removing a path never decreases total resistance.
Option C is incorrect because changing the circuit structure inherently changes the equivalent impedance.
Option D is incorrect because zero resistance implies a short circuit.
B is correct тАФ Opening a parallel branch removes a path for current, thereby increasing the total equivalent resistance of the circuit.
Always remember that in parallel circuits, ReqтАЛ<min(R1тАЛ,R2тАЛ,R3тАЛ). If you lose a parallel path, the resistance must climb towards the value of the remaining smallest resistor.