Question

VARIABLE EQUATIONS & INEQUALITIES UNIT TEST:
THE ELECTRIC CURRENT, /(amps), PASSING THROUGH AN ELECTRONIC COMPONENT VARIES DIRECTLY WITH THE APPLIED VOLTAGE, V (volts), ACCORDING TO THE RELATIONSHIP V= IR WHERE R, IS THE RESISTANCE MEASURED IN Ohms(Ω).

WONG IS TRYING TO FIND OUT THE RESISTANCE, R, OF AN UNKNOWN COMPONENT. HE LABELS THE RESISTANCE OF THE UNKNOWN COMPONENT AS xΩ. THE RESISTANCE, R, OF A CIRCUIT CONTAINING THESE UNKNOWN COMPONENTS IS (5 X + 20) Ω. A 90-volt POTENTIAL DIFFERENCE ACROSS THE CIRCUIT PRODUCES A CURRENT OF 2.25 amps.
WHAT IS THE RESISTANCE OF THE UNKNOWN COMPONENT? EXPLAIN HOW YOU ARRIVED AT YOUR ANSWER. IN 1 OR 2 SHORT SENTENCES.
GPT-4o mini
To find the resistance of the unknown component, we can use Ohm's law (V = IR). Given that the total voltage (V) is 90 volts and the current (I) is 2.25 amps, we can calculate the total resistance (R) using the formula R = V/I.

So, R = 90 / 2.25 = 40 Ω.

Next, we know the total resistance of the circuit is (5x + 20) Ω, so we set it equal to the calculated resistance:

5x + 20 = 40.

Solving for x, we get 5x = 20, thus x = 4 Ω.

The resistance of the unknown component is 4 Ω.