a 1 ohm resistor, a 1000 resistor and a 2000 ohm resistor are connected in parallel. The total resistance is
1/R=1/1+1/1000+1/2000
2000/R=2000+2+1=2003
R=2000/20003 ohms
To find the total resistance (R_total) when resistors are connected in parallel, we can use the formula:
1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
Let's calculate the total resistance for the given resistors:
R1 = 1 ohm
R2 = 1000 ohms
R3 = 2000 ohms
1/R_total = 1/1 + 1/1000 + 1/2000
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 2000.
1/R_total = (2000/2000) + (2/2000) + (1/2000)
1/R_total = (2000 + 2 + 1) / 2000
1/R_total = 2003/2000
To find the reciprocal of 1/R_total, we would take the reciprocal of the fraction:
R_total = 2000/2003
Therefore, the total resistance when the resistors are connected in parallel is approximately 0.999 ohms.
To calculate the total resistance of resistors connected in parallel, you can use the formula:
1/R_total = 1/R_1 + 1/R_2 + 1/R_3 + ...
In this case, you have three resistors connected in parallel: a 1 ohm resistor, a 1000 ohm resistor, and a 2000 ohm resistor.
Step 1: Calculate the reciprocals of the resistances.
Reciprocal of 1 ohm resistor: 1/R_1 = 1/1 = 1
Reciprocal of 1000 ohm resistor: 1/R_2 = 1/1000 = 0.001
Reciprocal of 2000 ohm resistor: 1/R_3 = 1/2000 = 0.0005
Step 2: Add the reciprocals of the resistances.
1/R_total = 1 + 0.001 + 0.0005 = 1.0015
Step 3: Take the reciprocal of the sum.
R_total = 1/1.0015 ≈ 0.9985 ohms
Therefore, the total resistance of the three resistors connected in parallel is approximately 0.9985 ohms.