If three resistor 2n, 3n and 5n are connected in parallel in a circuit. Calculate the equivalent resistance of the combination
To calculate the equivalent resistance (R_eq) of resistors connected in parallel, you use the formula:
1/R_eq = 1/R_1 + 1/R_2 + 1/R_3 + ...
In this case, the resistors are 2n, 3n, and 5n. So the equivalent resistance is:
1/R_eq = 1/2n + 1/3n + 1/5n
To add fractions with different denominators, you need to find a common denominator. In this case, the least common denominator is 30n. So the equation becomes:
1/R_eq = (15/30n) + (10/30n) + (6/30n)
Adding these fractions together:
1/R_eq = (15 + 10 + 6) / 30n
1/R_eq = 31/30n
To get the R_eq, you take the reciprocal of both sides:
R_eq = 30n / 31
Therefore, the equivalent resistance of the combination is 30n/31.