three resistors of 2ohm, 3ohm and 4 ohm are connected in (a) series (b) parallel. find the equivalent resistance in each case
SERIES: 2+3+4 OHM
PARALLEL: (1/r)=1/2 + 1/3 + 1/4
R=2*3*4/(3*4+4*2+3*2)/(2*3*4)
=26/24 OHMS
all in parallel
(a) In series:
To find the equivalent resistance in a series circuit, we simply add up the individual resistances.
So, for the given resistances of 2 ohm, 3 ohm, and 4 ohm connected in series, the equivalent resistance (R_eq) is:
R_eq = 2 ohm + 3 ohm + 4 ohm
= 9 ohm
Therefore, the equivalent resistance in a series circuit is 9 ohm.
(b) In parallel:
To find the equivalent resistance in a parallel circuit, we use the formula:
1/R_eq = 1/R1 + 1/R2 + 1/R3
Where R1, R2, and R3 are the individual resistances.
In this case, the given resistances are 2 ohm, 3 ohm, and 4 ohm. Substituting these values into the formula, we have:
1/R_eq = 1/2 ohm + 1/3 ohm + 1/4 ohm
To simplify, we find the least common multiple (LCM) of 2, 3, and 4, which is 12:
1/R_eq = 6/12 ohm + 4/12 ohm + 3/12 ohm
= 13/12 ohm
Taking the reciprocal of both sides, we find:
R_eq = 12/13 ohm
Therefore, the equivalent resistance in a parallel circuit is 12/13 ohm.
To find the equivalent resistance in each case, we can use the formulas for resistors in series and resistors in parallel.
a) Resistors in series: To find the equivalent resistance (R_eq) of resistors connected in series, we add up the individual resistances.
R_eq = R1 + R2 + R3
So, for the given resistors of 2 ohm, 3 ohm, and 4 ohm connected in series:
R_eq = 2 + 3 + 4 = 9 ohm
Therefore, the equivalent resistance when the resistors are connected in series is 9 ohm.
b) Resistors in parallel: To find the equivalent resistance (R_eq) of resistors connected in parallel, we use the formula:
1/R_eq = 1/R1 + 1/R2 + 1/R3
So, for the given resistors of 2 ohm, 3 ohm, and 4 ohm connected in parallel:
1/R_eq = 1/2 + 1/3 + 1/4
To simplify this, we can find a common denominator:
1/R_eq = (6/12) + (4/12) + (3/12)
Combining the fractions:
1/R_eq = 13/12
To find R_eq, we take the reciprocal:
R_eq = 12/13 ≈ 0.923 ohm (rounded to three decimal places)
Therefore, the equivalent resistance when the resistors are connected in parallel is approximately 0.923 ohm.