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The electric current, I (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 (5x+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.

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To find the resistance \( x \) of the unknown component, we start by using Ohm's Law, which states that the relationship between voltage \( V \), current \( I \), and resistance \( R \) is given by:

\[ V = I \cdot R \]

In this case, we are given:

  • The voltage \( V = 90 \) volts
  • The current \( I = 2.25 \) amps

We can plug these values into Ohm's Law to find the total resistance \( R \):

\[ 90 = 2.25 \cdot R \]

To isolate \( R \), we can divide both sides by \( 2.25 \):

\[ R = \frac{90}{2.25} \]

Calculating that gives:

\[ R = 40 , \Omega \]

Now, we know that the total resistance \( R \) is expressed as \( R = 5x + 20 \). Since we have found \( R = 40 , \Omega \), we can set up the following equation:

\[ 5x + 20 = 40 \]

Now, we will solve for \( x \):

  1. Subtract 20 from both sides:

\[ 5x = 40 - 20 \]

This simplifies to:

\[ 5x = 20 \]

  1. Next, divide each side by 5:

\[ x = \frac{20}{5} \]

So, we find:

\[ x = 4 , \Omega \]

Thus, the resistance of the unknown component is \( \boxed{4 , \Omega} \).

Summary of the steps:

  1. Applied Ohm's Law to find the total resistance of the circuit using given voltage and current.
  2. Set the total resistance equal to the expression involving the unknown resistance and solved for \( x \).