Resistor given as r1 r2 and r3 are connected in series to a battery v draw a circuit diagram showing the arrangement derive an expression for the equivalent resistance of the combination.
Answers
Answer:
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The equivalent resistance of in series combination:
Explanation:
The total potential difference across a combination of resistors in a series combination is equal to the sum of potential differences across the individual resistors.
Let R1, R2, R3 be the resistances in a circuit.
Let I is the current flowing through the circuit.
Let V1, V2, V3 be the potential differences across the circuit.
By defination,
V = V1 + V2 + V3
Let ' I ' be the current in the circuit. The current flowing through each resistor is also I. It is possible to replace the three resistors in a series combination by an equivalent resistor of resistance R.
By Ohm's law,
V = IR
where
V = potential difference across a combination
I = current flowing through a circuit
R = resistance of resistor
By applying Ohm's law to the three resistors respectively, we have
V1 = IR1
V2 = IR2
V3 = IR3
But
V = V1+ V2 + V3
IR = IR1 + IR2 + IR3
Divide each term by I
R = R1 + R2 + R3
This is the equivalent resistance of the series combination.
Refer to the following attachment:
