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In a series circuit consisting of three resistors R1, R2, and R3, if the resistance R2 is replaced by a wire of zero resistance (short circuit), the total resistance of the circuit will _____
Increase
Decrease
Remain unchanged
Become zero
Decrease
In a series circuit, the total equivalent resistance is the algebraic sum of individual resistances. When a resistor is replaced by a wire of zero resistance, the total resistance decreases by the magnitude of that specific resistor.
In a series circuit, the total equivalent resistance is the algebraic sum of individual resistances. When a resistor is replaced by a wire of zero resistance, the total resistance decreases by the magnitude of that specific resistor.
ReqтАЛ=R1тАЛ+R2тАЛ+R3тАЛ тАФ Formula for equivalent resistance of series resistors
RshortтАЛ=0╬й тАФ Resistance of an ideal short circuit
According to Kirchhoff's Voltage Law and the properties of series circuits, the total resistance ReqтАЛ is defined as R1тАЛ+R2тАЛ+R3тАЛ. By replacing R2тАЛ with a short circuit (a wire with 0╬й resistance), the new equivalent resistance becomes ReqтА▓тАЛ=R1тАЛ+0+R3тАЛ. Since R2тАЛ>0, it follows that ReqтА▓тАЛ<ReqтАЛ.
Total resistance in a series circuit is always greater than any individual resistor value.
A short circuit effectively bypasses a component, reducing the total path impedance.
Short circuiting a component in series leads to an increase in total current I=ReqтАЛVтАЛ.
Simple method for circuit analysis
Easy identification of nodes
Replacing a resistor with a wire can lead to high current flow if not accounted for
May cause overheating in real-world components
Troubleshooting electrical faults
Designing variable resistance circuits
An ideal short circuit has exactly 0╬й resistance.
Option A is incorrect because adding resistance increases total resistance, not removing it.
Option C is incorrect because R2тАЛ is not zero, so removing it alters the sum.
Option D is incorrect because R1тАЛ and R3тАЛ remain in the circuit.
B is correct тАФ The total resistance of the series circuit decreases because the term R2тАЛ is removed from the summation of resistances.
Always remember that in series circuits, the total resistance is the sum of parts; in parallel circuits, the total resistance is always less than the smallest individual resistor.