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. (2 points)

Answer 1

To find the resistance \( x \) of the unknown component, we can use Ohm's law, which is given by the equation:

\[ V = IR \]

where \( V \) is the voltage in volts, \( I \) is the current in amps, and \( R \) is the resistance in ohms.

In this case, we know:

• The voltage \( V = 90 \) volts
• The current \( I = 2.25 \) amps
• The total resistance of the circuit \( R = 5x + 20 \) ohms

First, we can calculate the total resistance using Ohm's law:

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

Calculating this gives:

\[ R = 40 \text{ ohms} \]

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

\[ 5x + 20 = 40 \]

Next, we solve for \( x \):

1. Subtract 20 from both sides: \[ 5x = 20 \]

2. Divide both sides by 5: \[ x = 4 \]

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

In summary, we arrived at the answer by using Ohm's law to find the total resistance of the circuit, and then we compared that to the expression for the resistance given in terms of the unknown component's resistance \( x \). Solving the resulting equation gave us the value of \( x \).