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The amount of resistance, y, in a circuit varies inversely to the current, x, in the circuit. When 10 ohms of resistance are used in the circuit, 12 amperes of current are present. When 5 ohms of resistance are used in the same circuit, 24 amperes of current are present.

How many ohms of resistance are used in the circuit when 15 amperes of current are present? Round your answer to the nearest tenth, if necessary.

Respuesta :

Cricetus

Answer:

8 Ohms Resistance

Step-by-step explanation:

Let the Resistance is represented by f(x) and The current in x. hence we are given that

[tex]f(x)∝\frac{1}{x} [/tex]

Using constant of proportionality k we can say that  

[tex]f(x) = k\times \frac{1}{x}  [/tex]

where k is always constant for all values of x and f(x)

now we are given that for x = 12, we have f(x) = 210

This will help us to determine k , once we have the value of k , we can determine the f(x) for x = 15

Hence Now we have  

[tex]f(x) = 10 , x = 102 [/tex]

putting them into

[tex]f(x) = k\times \frac{1}{x}  [/tex]

[tex]10=k\times \frac{1}{12}   [/tex]

[tex]k=120 [/tex]

Hence we now know the value of k as 120

Now we find f(x) at x=15

[tex]f(x)= 120 \times \frac{1}{15}  [/tex]

[tex]f(x) = \frac{120}{15}   [/tex]

[tex]f(x) = 8  [/tex]

Hence this is our answer  8 Ohms of Resistance will be used.

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