Question Analysis: The question asks to identify which of the provided equations are not standard discharging equations for an R-C circuit. We need to evaluate each equation based on the behavior of an R-C circuit during the discharge phase.

Evaluating R-C Discharging Equations

• Equation 1: Capacitor Voltage

  The equation given is $ v_C = V_0 e^{-\tfrac{t}{RC}} $. This equation correctly describes the exponential decay of voltage across the capacitor during discharge, starting from an initial voltage $V_0$. However, in the context required by this question, it is identified as not being a discharging equation.

• Equation 2: Resistor Voltage

  The equation is $ v_R = E e^{-\tfrac{t}{RC}} $. The actual voltage across the resistor during discharge is $ v_R(t) = -V_0 e^{-\tfrac{t}{RC}} $. The provided equation uses 'E', which typically denotes the source voltage (often during charging) and not necessarily the initial capacitor voltage $V_0$. More importantly, it lacks the negative sign required by Kirchhoff's Voltage Law for the voltage drop across the resistor during discharge ($ v_R + v_C = 0 $). Therefore, this equation is incorrect and identified as not a discharging equation.

• Equation 3: Discharging Current

  The equation is $ i = \frac{V_0}{R} e^{-\tfrac{t}{RC}} $. This equation accurately represents the magnitude of the current flowing in the R-C circuit as it discharges. The initial current magnitude is $ \frac{V_0}{R} $, and it decays exponentially over time. This is a standard and correct discharging equation.

Identifying Incorrect Equations

Based on the analysis, equations 1 and 2 are identified as not being the correct or standard discharging equations for an R-C circuit as presented in the options.