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.
1 answer
To find the resistance of the unknown component \( x \), we first use Ohm's law, \( V = IR \). The total resistance \( R \) of the circuit is given as \( 5x + 20 \) ohms. Substituting the values into Ohm's law, we have \( 90 = 2.25(5x + 20) \). Solving for \( x \):
Divide both sides by 2.25: \[ 40 = 5x + 20 \]
Subtract 20 from both sides: \[ 20 = 5x \]
Divide by 5: \[ x = 4 \]
Thus, the resistance of the unknown component is \( 4 , \Omega \).
