Sure! Let's solve the problem step-by-step.
### Step 1: Identify Given Data and Unknowns
Givens:
- Voltage ([tex]\(V\)[/tex]): 10 volts (V)
- Power ([tex]\(P\)[/tex]): 0.5 watts (W)
Unknown:
- Resistance ([tex]\(R\)[/tex]): ?
### Step 2: List the Relevant Equation
The power dissipated by a resistor in an electrical circuit can be described using the formula:
[tex]\[ P = \frac{V^2}{R} \][/tex]
Where:
- [tex]\(P\)[/tex] is the power (in watts),
- [tex]\(V\)[/tex] is the voltage (in volts),
- [tex]\(R\)[/tex] is the resistance (in ohms, [tex]\(\Omega\)[/tex]).
### Step 3: Rearrange the Equation to Solve for Resistance
We need to solve for [tex]\(R\)[/tex]. Rearrange the formula to isolate [tex]\(R\)[/tex] on one side:
[tex]\[ R = \frac{V^2}{P} \][/tex]
### Step 4: Plug in the Given Values
Substitute the given values for voltage and power into the equation:
[tex]\[ R = \frac{(10 \, \text{V})^2}{0.5 \, \text{W}} \][/tex]
### Step 5: Perform the Calculation
1. Square the voltage:
[tex]\[ V^2 = (10 \, \text{V})^2 = 100 \, \text{V}^2 \][/tex]
2. Divide by the power:
[tex]\[ R = \frac{100 \, \text{V}^2}{0.5 \, \text{W}} \][/tex]
3. Simplify the fraction:
[tex]\[ R = 200 \, \Omega \][/tex]
### Step 6: State the Final Answer with Correct Units
The resistance of the bulb is:
[tex]\[ R = 200 \, \Omega \][/tex]
So, the resistance of the bulb in this circuit is 200 ohms.
