Question

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.

Answer 1

To find the resistance \( x \) of the unknown component, we can use Ohm's Law, which states:

\[
V = IR
\]

Where:
- \( V \) is the voltage (90 volts),
- \( I \) is the current (2.25 amps),
- \( R \) is the total resistance of the circuit, which is given as \( (5x + 20) \, \Omega \).

From the relationship, we can rearrange the equation to find \( R \):

\[
R = \frac{V}{I}
\]

Now, substituting the values for \( V \) and \( I \):

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

Calculating this gives:

\[
R = 40 \, \Omega
\]

Now, we set this equal to the expression for the total resistance:

\[
5x + 20 = 40
\]

Next, we'll solve for \( x \):

\[
5x + 20 = 40
\]

Subtracting 20 from both sides:

\[
5x = 40 - 20
\]

\[
5x = 20
\]

Dividing both sides by 5:

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

\[
x = 4
\]

Thus, the resistance of the unknown component is:

\[
\boxed{4 \, \Omega}
\]

### Summary of the Steps:
1. Use Ohm's Law to find the total resistance \( R \) using the current and voltage.
2. Set the found resistance equal to the expression for resistance given in the problem and solve for \( x \).