derive the formula 1/R = 1/R1 + 1/R2
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Answers
ammeter reading when connected to ina series to the circuit I=I1+I2+I3
voltmeter reading must be constant V=IR
I1=V/R1
I2=V/R2
I3=V/R3
on adding the three equation
I1+I2+I3=V/R1+V/R2+V/R3
I= v[1/R1+1/R2+1/R3]
I/V=". "
SO R=1/R1+1/R2+1/R3. V/I=R
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Derivation for the formula for the resultant resistance when the resistors are in the parallel combination .
Consider 2 resistors R1 and R2 to be connected n parallel combination.
Two resistors are said to be in the parallel combination when the both of the ends of the resistors are collected and tied together to have the resistors with common potential difference.
We know that , From Ohm's Law , V = IR Then for parallel combination let R(p) be resultant resistance of parallel combination, and I be resultant current. So, V = IR(p)
or I = V/R(p) _________________[ 1]
Since in parallel combination the potential difference will be the same ,let it be considered as V .
Let current through resistors R1 and R2 be I1 and I2 respectively.
Then, => I = I1 + I2 _________________[2]
Then, substituting equation [ 2] in equation [ 1] .
=> I1 + I2 = V/R1 + V/R2
=> I = V [ 1/R1 + 1/R2 ]
From equation [ 1] putting , I = V/R(p)
=> V/R(p) = V [ 1/R1 + 1/R2 ]
=> 1/R(p) = 1/R1 + 1/R2
Hence , the resultant resistance for resistors in parallel can be given by the equation 1/R(p) = 1/R1 + 1/R2
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