Question #42738

A specialized liquid-electrolyte battery of EMF $E = 12 \text{ V}$ is connected across an external resistor $R = 4 \ \Omega$. Due to pressure-induced viscosity changes, the average ion mobility in the electrolyte is inversely proportional to the hydrostatic pressure difference $\Delta P$ between the bottom and top of the electrolyte column. Consequently, the internal resistance $r$ of this battery depends on $\Delta P$. When the battery is at rest on the ground, its internal resistance is $r_0 = 2 \ \Omega$. The entire setup is placed inside an elevator. If the elevator accelerates upwards with a constant acceleration $a = 5 \text{ m/s}^2$, calculate the terminal voltage across the battery. (Assume the density of the electrolyte and the height of the column remain constant, and take $g = 10 \text{ m/s}^2$).