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.