To solve the problem of finding the resistance \( R \) of an unknown component in a circuit where the current \( I \) varies directly with the voltage \( V \), you can use Ohm's Law, which states that:
\[ V = I \cdot R \]
Given the problem, we need to first set up the equation using the provided information.
You mentioned a current represented by \( 5x + 20 \) and a voltage of 90 volts. To apply Ohm’s Law, we rearrange the formula to solve for resistance:
\[ R = \frac{V}{I} \]
Where \( V \) is the voltage (90 volts) and \( I \) is the current \( (5x + 20) \).
Substituting the values into the equation:
\[ R = \frac{90}{5x + 20} \]
Now, to find the resistance in this system, we would need to determine the value of \( x \). However, since you didn’t provide a specific value for \( x \), the expression for the resistance simply remains:
\[ R = \frac{90}{5x + 20} \]
This tells us how the resistance varies with the different values of \( x \).
Explanation of the Process
- Understanding the Equation: We outlined Ohm’s Law and identified the relationship among current, voltage, and resistance.
- Substituting Known Values: We substituted the values provided for voltage and current into the resistance formula.
- Final Expression: Without a specific value for \( x \), we were unable to compute a numerical value for \( R \). However, the equation \( R = \frac{90}{5x + 20} \) encapsulates the relationship clearly.
Next Step
If you can provide a specific value for \( x \), we could compute a numerical resistance value. If not, this formula allows you to explore how changing \( x \) affects the resistance \( R \).
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