Given:

• Two resistors $R_1$ and $R_2$ are connected in parallel.
• The applied voltage across the parallel combination is $V = 200$ V.
• The total current drawn is $I_{\text{total}} = 25$ A.
• The power dissipated by one of the resistors (let's assume $R_1$) is $P_1 = 1500$ W.

Step 1: Find $R_1$

We can use the power formula to find $R_1$: $P_1 = \frac{V^2}{R_1}$ Rearranging for $R_1$: $R_1 = \frac{V^2}{P_1} = \frac{200^2}{1500} = \frac{40000}{1500} \approx 26.67 \, \Omega$

Step 2: Find the current through $R_1$

Using Ohm's law, the current through $R_1$ is: $I_1 = \frac{V}{R_1} = \frac{200}{26.67} \approx 7.5 \, \text{A}$

Step 3: Find the current through $R_2$

The total current is the sum of the currents through $R_1$ and $R_2$: $I_{\text{total}} = I_1 + I_2$ $25 = 7.5 + I_2$ Solving for $I_2$: $I_2 = 25 - 7.5 = 17.5 \, \text{A}$

Step 4: Find $R_2$

Using Ohm's law for $R_2$: $R_2 = \frac{V}{I_2} = \frac{200}{17.5} \approx 11.43 \, \Omega$

Final Answer:

• $R_1 \approx 26.67 \, \Omega$
• $R_2 \approx 11.43 \, \Omega$

Would you like further details or have any questions?

Here are some related questions to consider:

1. How is power dissipated in a resistor related to current and resistance?
2. What would happen to the total current if the voltage increased to 300V?
3. How would the problem change if the resistors were connected in series instead of parallel?
4. How do you calculate the equivalent resistance of parallel resistors?
5. What are the implications of using resistors with very different resistances in a parallel circuit?

Tip: In a parallel circuit, the voltage across each resistor is the same as the source voltage, but the current splits according to the resistances.