To find the resistance \( R \) of the unknown components, we can use Ohm's Law, which states:
\[ V = I \times R \]
where:
- \( V \) is the voltage (90 volts),
- \( I \) is the current (2.25 amps),
- \( R \) is the resistance.
We need to find \( R \) in terms of the given expression \( 5x + 20 \).
First, we can rearrange Ohm's Law to solve for \( R \):
\[ R = \frac{V}{I} \]
Substituting the given values:
\[ R = \frac{90 , \text{volts}}{2.25 , \text{amps}} = 40 , \Omega \]
Now we equate this to the expression for the resistance given by the unknown components:
\[ 5x + 20 = 40 \]
Next, we solve for \( x \):
\[ 5x + 20 = 40 \] \[ 5x = 40 - 20 \] \[ 5x = 20 \] \[ x = \frac{20}{5} = 4 \]
Now that we have \( x = 4 \), we can substitute it back to find the resistance:
\[ R = 5x + 20 = 5(4) + 20 = 20 + 20 = 40 , \Omega \]
Thus, the resistance of the unknown component is:
\[ \boxed{40 , \Omega} \]
0 answers