Question

Find the value of r1 that makes req = 40?

Answer 1

The value of
`\( r_1 \) that makes \( \text{req} = 40 \) is \( r_1 = 30 \) ohms.`

Step-by-step explanation:

The total resistance
`(\( \text{req} \))` in a parallel circuit is given by the reciprocal of the sum of the reciprocals of individual resistances. For two resistors
`(\( r_1 \) and \( r_2 \)) in parallel, the formula is \( \frac{1}{\text{req}} = (1)/(r_1) + (1)/(r_2) \).` In this case, the given condition is
`\( \text{req} = 40 \).`

We can express this mathematically as
`\( (1)/(40) = (1)/(r_1) + (1)/(r_2) \)`. Since only
`\( r_1 \) is unknown, we can set \( r_2 \) to a known value, say \( r_2 = 60 \)` ohms. Solving for
`\( r_1 \), we find that \( r_1 = 30 \)`ohms.

Therefore, when
`\( r_1 = 30 \) ohms and \( r_2 = 60 \)` ohms are connected in parallel, the total resistance
`\( \text{req} \)` becomes 40 ohms. This solution satisfies the given condition, and it illustrates how to find the value of
`\( r_1 \)`using the formula for the total resistance in a parallel circuit.