obtain an expression for the effictive resistance when a number of resistors are connected in series?explain it qith the help of a diagram
Answers
Explanation:
In
R1, R2 and R3 are the three resistors connected in series between points C and D as shown. I is the current and V is the PD across points C and D.
Then Rs is the effective resistance in a circuit and V1, V2 and V3 are the potentials across the three resistors such that
V = V1 + V2 + V3 ---- (1)
Using Ohm's law, the total potential difference
V = I Rs
and V1 = IR1, V2 = IR2 and V3 = IR3
Substituting these values in equation 1, we get
IRS = IR1 + IR2 + IR3
∴ RS = R1 + R2 + R3
For n number of resistors connected in series,
RS = R1 + R2 + R3 + R4 + ----- + Rn
2. Expression for the resistors in parallel:
R1, R2 and R3 are the three resistors connected in parallel between points C and D as shown in the figure.
Let I1, I2 and I3 be the currents passing through R1, R2 and R3, respectively.
Let V be the potential difference between points C and D. The current I will be given by
I = I1 + I2 + I3 ----- (1)
Let RP be the effective resistance in the circuit.
Using Ohm's law, we get
begin mathsize 12px style straight I subscript 1 equals straight V over straight R subscript 1 comma space straight I subscript 2 equals straight V over straight R subscript 2 comma space space straight I subscript 3 equals straight V over straight R subscript 3 space and space space straight I equals straight V over straight R subscript straight P end style
Putting these values in equation 1, we get
begin mathsize 12px style fraction numerator straight V space over denominator straight R subscript straight P end fraction equals fraction numerator straight V space over denominator straight R subscript 1 end fraction plus fraction numerator straight V space over denominator straight R subscript 2 end fraction plus fraction numerator straight V space over denominator straight R subscript 3 end fraction
therefore fraction numerator 1 space over denominator straight R subscript straight P end fraction equals fraction numerator 1 space over denominator straight R subscript 1 end fraction plus fraction numerator 1 space over denominator straight R subscript 2 end fraction plus fraction numerator 1 space over denominator straight R subscript 3 end fraction end style
For n number of resistors connected in parallel, we get begin mathsize 12px style fraction numerator 1 space over denominator straight R subscript straight P end fraction equals fraction numerator 1 space over denominator straight R subscript 1 end fraction plus fraction numerator 1 space over denominator straight R subscript 2 end fraction plus fraction numerator 1 space over denominator straight R subscript 3 end fraction..... plus fraction numerator 1 space over denominator straight R subscript straight n end fraction end style
Answered by | 24th Jul, 2017, 11:58: AM
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