https://file.aiquickdraw.com/mathbot/file/17273175241174hcqenkg.jpg

The circuit shown in the image appears to have the following information:

- Voltage across the circuit: \( V = 490V \)
- Current through the circuit: \( I = 0.25A \)
- Resistance \( R_2 = 10 \Omega \)
- \( R_1 \) and \( R_3 \) are unknown values to be determined.

The problem asks to find the missing values of \( R_1 \) and \( R_3 \), as well as the total resistance of the circuit.

### Step 1: Use Ohm's Law to find the total resistance
From Ohm’s Law, we know:

\[
V = IR_{\text{total}}
\]

Where:
- \( V \) is the total voltage
- \( I \) is the current
- \( R_{\text{total}} \) is the total resistance

Rearranging for \( R_{\text{total}} \):

\[
R_{\text{total}} = \frac{V}{I} = \frac{490V}{0.25A} = 1960 \Omega
\]

### Step 2: Express the total resistance in terms of \( R_1 \), \( R_2 \), and \( R_3 \)
Since the circuit appears to be in series, the total resistance is the sum of all individual resistances:

\[
R_{\text{total}} = R_1 + R_2 + R_3
\]

Substitute the known values:

\[
1960 \Omega = R_1 + 10 \Omega + R_3
\]

This simplifies to:

\[
R_1 + R_3 = 1950 \Omega
\]

### Step 3: Find the relationship between \( R_1 \) and \( R_3 \)
To solve for the individual values of \( R_1 \) and \( R_3 \), additional information such as the voltage drop across or current through \( R_1 \) or \( R_3 \) is needed. However, without more specific data, there are infinite possibilities for \( R_1 \) and \( R_3 \) as long as they satisfy:

\[
R_1 + R_3 = 1950 \Omega
\]

This means any pair of values \( R_1 \) and \( R_3 \) that add up to 1950 ohms will be valid.

### Conclusion:
- The total resistance is \( 1960 \Omega \).
- \( R_1 + R_3 = 1950 \Omega \), so the values of \( R_1 \) and \( R_3 \) can vary as long as their sum equals 1950 ohms.

Do you want more details, or do you have any specific questions?

### 5 Related Questions:
1. How would the circuit change if it were a parallel circuit instead of a series?
2. How can we measure the voltage drop across each resistor using a voltmeter?
3. What effect would changing the value of \( R_2 \) have on the total resistance?
4. How does the power consumed in each resistor depend on the current and resistance values?
5. How could we experimentally verify the values of \( R_1 \) and \( R_3 \) in the lab?

### Tip:
When dealing with circuits, always double-check the configuration (series or parallel) as it affects how you calculate total resistance and other parameters.

Find the missing values R1, R3, and the total resistance in a series circuit with a voltage of 490V, a current of 0.25A, and a known resistance R2 = 10Ω.

Learn how to find the missing resistances R1 and R3 in a series circuit using Ohm's Law. The problem involves a voltage of 490V, a current of 0.25A, and a known resistance R2 = 10Ω. Suitable for students in Grades 9-12.

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