Given Circuit:

The given circuit consists of a voltage source, resistors, and a switch. We are required to find the voltage across the 10 ohm resistor and the current passing through it.

Solution:

To find the voltage across the 10 ohm resistor and the current passing through it, we need to analyze the given circuit step by step.

Step 1: Determine the Total Resistance (R_total):

To find the total resistance, we need to calculate the resistance in series and parallel connections.

In the given circuit, the resistors R₁ and R₂ are connected in series, so their resistances add up:
R_total = R₁ + R₂ = 20 ohms

Step 2: Calculate the Current (I_total):

To find the current passing through the circuit, we can use Ohm's Law:

I = V / R

Here, V is the voltage across the voltage source and R is the total resistance.

Assuming the voltage source provides an output of 10 volts, we can calculate the current passing through the circuit:

I_total = 10 V / 20 ohms = 0.5 A

Step 3: Determine the Voltage across the 10 ohm Resistor:

Since the 10 ohm resistor is connected in series with the 20 ohm resistor, the same current passes through both resistors.

Using Ohm's Law, we can calculate the voltage across the 10 ohm resistor:

V_10ohm = I_total * R_10ohm = 0.5 A * 10 ohms = 5 V

Conclusion:

The voltage across the 10 ohm resistor is 5 volts, and the current passing through it is 0.5 amperes.