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 hundredth, if necessary. ohms

Question

Mathematics

Alessandro Mullen

23 June, 22:13

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 hundredth, if necessary. ohms

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Evans · Answer 1

Let k be a constant of proportionality. We can use the given information to write two equations:

24 = k/5 and 12 = k/10.

Solving for k gives k = 120 in both cases.

Let R be the unknown resistance when the current is 15 amperes:

15 = 120/R.

R = 120/15

R = 8 ohms.