Calculate the current and voltage shown (i.e., across R5).

Steps to Solve

1. Identify Resistor Values First, we need to identify the values of the resistors based on the student's number. Using the equations provided:

   • $R_1 = x_1 + 2$
   • $R_2 = x_2 + 2$
   • $R_3 = x_3 + 2$
   • $R_4 = x_4 + 2$
   • $R_5 = x_5 + 2$

2. Calculate Total Resistance in Each Branch To calculate the current through each branch of the bridge circuit, we can use the values of the resistors to determine the equivalent resistances in the branches:

   • Calculate $R_a = R_1 + R_2$ (for the top branch)
   • Calculate $R_b = R_3 + R_4$ (for the bottom branch)

3. Use Voltage Division to Find Voltage Across R5 The voltage across resistor $R_5$ can be calculated using the voltage division rule. The total voltage $V = 10V$ is across both branches:

   • The voltage across $R_5$, $v_x$, can be computed as:
     $$ v_x = V \times \frac{R_5}{R_a + R_b} $$

4. Calculate the Current through R5 Using Ohm’s law, we can find the current through the resistor $R_5$:

   • The current $i_x$ through $R_5$ is given by:
     $$ i_x = \frac{v_x}{R_5} $$

5. Substitute and Simplify Equations Now, substitute the values into the equations and simplify to solve for $i_x$ and $v_x$. This involves recalculating using the original resistor values derived from the student's number.