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To calculate the voltage across the \( 2 \, \Omega \) resistor in the circuit with a supply voltage of \( 10 \, V \), let's go step by step:

### 1. Identify resistances and voltage
The circuit consists of three resistors:
- \( R_1 = 2 \, \Omega \)
- \( R_2 = 1 \, \Omega \)
- \( R_3 = 2 \, \Omega \)

The resistors \( R_1 \) and \( R_2 \) are in series, and the combination is in parallel with \( R_3 \). The total supply voltage is \( 10 \, V \).

### 2. Calculate the equivalent resistance of the series combination
The series combination of \( R_1 \) and \( R_2 \) gives:
\[
R_{\text{series}} = R_1 + R_2 = 2 \, \Omega + 1 \, \Omega = 3 \, \Omega
\]

### 3. Find the total resistance of the circuit
The equivalent resistance of the circuit can be found by combining \( R_{\text{series}} \) with \( R_3 \) (which are in parallel). The formula for parallel resistances is:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{R_{\text{series}}} + \frac{1}{R_3}
\]
Substituting values:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{3 \, \Omega} + \frac{1}{2 \, \Omega} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}
\]
Thus, the total resistance is:
\[
R_{\text{total}} = \frac{6}{5} = 1.2 \, \Omega
\]

### 4. Calculate the total current in the circuit
Using Ohm's law, the total current \( I \) is:
\[
I = \frac{V}{R_{\text{total}}} = \frac{10 \, V}{1.2 \, \Omega} = 8.33 \, A
\]

### 5. Find the current through \( R_3 \) (the \( 2 \, \Omega \) resistor)
Since \( R_{\text{series}} \) and \( R_3 \) are in parallel, the voltage across \( R_3 \) is the same as the voltage across \( R_{\text{series}} \). Let’s first calculate the voltage across \( R_{\text{series}} \), which will be the same as across \( R_3 \).

Using the current divider rule:
\[
V_{R_3} = I \times R_{\text{parallel}} = 8.33 \, A \times \left( \frac{R_{\text{parallel}}}{R_{\text{parallel}} + R_3} \right) =8. 
thus

Calculate the voltage across a 2Ω resistor where the supply voltage is 10V.

Find out how to calculate the voltage across a 2Ω resistor in a mixed series-parallel circuit with a 10V supply. This solution involves applying Ohm's law, calculating total resistance, and using the current divider rule, ideal for Grades 9-12 physics students.

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