. Two resistors are connected in parallel and a voltage of 200 Volts is
applied to the terminals. The total current taken is 25A and the power
dissipated in one of the resistor is 1500W. Determine the resistance of
each element?

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.

Two resistors are connected in parallel and a voltage of 200 Volts is applied to the terminals. The total current taken is 25A and the power dissipated in one of the resistors is 1500W. Determine the resistance of each element?

Find the resistance of two resistors connected in parallel with a 200V supply and a total current of 25A. The power dissipated in one resistor is 1500W. Step-by-step solution using Ohm's law and power dissipation formula, suitable for high school physics and electrical engineering students.

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