A simple circuit contains a 10 V battery connected with wires to a small bulb. If the power dissipated by the bulb is 0.5 W, what is the resistance of the bulb?

- Identify all data (givens and unknowns).
- List equations used.
- Show all your work.
- Include units and the proper number of significant digits.



Answer :

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.

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