A battery has a variable EMF E depending on the amount of electrochemical energy stored in it, U : `E=E_0[V/V_0]^(1/3)` , where`E_0` is the EMF of the battery when it has the maximum possible energy, `V_0` , stored in it. The internal resistance of the battery is negligible. The battery, with energy stored in it, is connected with a resistance R and the switch is closed at . Choose the correct option(s):

Options

A. The EMF of the battery decreases linearly with time
B. The rate of heat dissipation in the resistance decreases linearly with time
C. The energy stored in the battery runs out at `t=(3V_0R)/(E_0^2)`
D. The total heat dissipated in the resistance until `t=(3V_0R)/(2E_0^2) is 7/8 V_0`

Explanation

To solve the problem, we need to analyze the relationship between the electromotive force (EMF) of the battery, the energy stored in it, and the time as the battery discharges through a resistor.

### Step-by-Step Solution:

1. **Understand the EMF Equation**:
The EMF of the battery is given by:
\[
E = E_0 \left( \frac{V}{V_0} \right)^{1/3}
...