What is the minimum number of 70 -Ohms resistors that must be connected in parallel to produce an equivalent resistance of 13 Ohms or less?
1/13>=k/70
70=>13k
k>70/13
k>6
If you have a curcuit consisting of 4 resistor of egual resistance senses and toltal voltage across all of them is 17v .what is the voltage across each of them?
To find the minimum number of 70-Ohms resistors that must be connected in parallel to produce an equivalent resistance of 13 Ohms or less, we need to determine the maximum resistance that each individual resistor should have in order to achieve this.
In a parallel circuit, the total resistance is given by the formula:
1/Req = 1/R1 + 1/R2 + ... + 1/Rn
Where Req is the equivalent resistance and R1, R2, ..., Rn are the individual resistances.
We want the equivalent resistance, Req, to be 13 Ohms or less. So we can rewrite the formula as:
1/13 ≤ 1/70 + 1/R2 + ...
Simplifying this inequality, we get:
1/R2 + ... ≥ 1/13 - 1/70
To find the maximum resistance for each resistor, we take the reciprocal of the difference on the right side:
1/R2 + ... ≥ 57/910
Rearranging the formula, we get:
R2 + ... ≤ 910/57
So each resistor's resistance should be less than or equal to 910/57 Ohms.
To find the minimum number of resistors required, we divide the total resistance by the maximum individual resistance:
Minimum number of resistors = 13 / (910/57)
Calculating this, we find:
Minimum number of resistors ≈ 0.81
Since the number of resistors must be a whole number, we have to round up to the nearest integer.
Therefore, the minimum number of 70-Ohms resistors that must be connected in parallel to produce an equivalent resistance of 13 Ohms or less is 1 resistor.