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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.

(2 points)

1 answer

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

\[ V = IR \]

In this case, we are given:

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

First, we can use Ohm's Law to find the total resistance \( R \) in the circuit:

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

Substituting the known values of \( V \) and \( I \):

\[ R = \frac{90 \text{ volts}}{2.25 \text{ amps}} = 40 \text{ ohms} \]

Now, we know that the total resistance of the circuit is also given by:

\[ R = 5x + 20 \]

Now we can set the two expressions for \( R \) equal to each other:

\[ 5x + 20 = 40 \]

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

  1. Subtract 20 from both sides:

\[ 5x = 40 - 20 \] \[ 5x = 20 \]

  1. Divide both sides by 5:

\[ x = \frac{20}{5} \] \[ x = 4 \]

Thus, the resistance of the unknown component is \( x = 4 \) ohms.

Answer: The resistance of the unknown component is 4Ω. I arrived at this answer by applying Ohm's Law to calculate total resistance from the given voltage and current, then setting it equal to the expression for total resistance involving \( x \) and solving for \( x \).