The circuit shows two resistors, X and R, connected in parallel to a voltage source E. An ammeter measures the total current flowing from the source.

Here's how to determine the value of X: The circuit shows two resistors, X and R, connected in parallel to a voltage source E. An ammeter measures the total current flowing from the source. The equivalent resistance (R_eq) for two resistors in parallel is given by: R_eq = (X · R)/(X + R) According to Ohm's Law, the voltage (E) across the parallel combination is the total current (I) multiplied by the equivalent resistance: E = I · R_eq Since the voltage source E is constant, we can set up equations for the two given scenarios. Scenario 1: Current I_1 = 3 \, A Resistance R_1 = 5 \, Equivalent resistance R_eq1 = (X · 5)/(X + 5) Voltage E = 3 · ((5X)/(X + 5)) = (15X)/(X + 5) (Equation 1) Scenario 2: Current I_2 = 6 \, A Resistance R_2 = 2 \, Equivalent resistance R_eq2 = (X · 2)/(X + 2) Voltage E = 6 · ((2X)/(X + 2)) = (12X)/(X + 2) (Equation 2) Now, we equate Equation 1 and Equation 2 since E is constant: (15X)/(X + 5) = (12X)/(X + 2) Since X is a resistance, X ≠ 0. We can divide both sides by X: (15)/(X + 5) = (12)/(X + 2) Cross-multiply to solve for X: 15(X + 2) = 12(X + 5) 15X + 30 = 12X + 60 Subtract 12X from both sides: 15X - 12X + 30 = 60 3X + 30 = 60 Subtract 30 from both sides: 3X = 60 - 30 3X = 30 Divide by 3: X = (30)/(3) X = 10 \, The value of X is 10 \, . The final answer is C. 10.