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 behavior of the battery with a variable EMF and how it affects the circuit connected to a resistance \( R \).

### Step-by-Step Solution:

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