What is the voltage at R2?

Steps to Solve

1. Identifying the Configuration

In the given circuit, resistors $R_1$ and $R_3$ are in parallel with resistors $R_2$ and $R_4$. We will first calculate the total resistance for the combinations.

2. Calculating the Total Resistance of R2 and R4

Since $R_2$ and $R_4$ are in series, their total resistance ($R_{24}$) is given by: $$ R_{24} = R_2 + R_4 = 480 \Omega + 470 \Omega = 950 \Omega $$

3. Calculating the Total Resistance of R1 and R3

Similarly, $R_1$ and $R_3$ are also in series. Their total resistance ($R_{13}$) is: $$ R_{13} = R_1 + R_3 = 680 \Omega + 1500 \Omega = 2180 \Omega $$

4. Finding Equivalent Resistance of R24 and R13

Now, the resistors $R_{24}$ and $R_{13}$ are in parallel. The equivalent resistance ($R_{eq}$) is calculated as: $$ \frac{1}{R_{eq}} = \frac{1}{R_{24}} + \frac{1}{R_{13}} $$ $$ \frac{1}{R_{eq}} = \frac{1}{950} + \frac{1}{2180} $$

5. Calculating the Voltage Across R2

Using the voltage divider rule, the voltage across $R_2$ (which is in series with $R_4$) can be calculated once we find the total current in the circuit. The total current ($I_{total}$) from the source can be found using: $$ I_{total} = \frac{V_{source}}{R_{eq}} = \frac{6 V}{R_{eq}} $$

Next, the voltage across $R_2$ can be calculated as: $$ V_{R2} = I_{total} \times R_2 $$