If i is current through the circuit and E is EMF of battery then power P at which chemical energy of battery is dissipated isa.P=E/i

Explanation of Power Dissipation in a Circuit

The formula given, $P = \frac{E}{i}$, represents the relationship between the power $P$ at which the chemical energy of the battery is dissipated, the electromotive force (EMF) $E$ of the battery, and the current $i$ flowing through the circuit.

1. Understanding the Formula:

   • $P$ stands for power, measured in watts (W).
   • $E$ represents the EMF of the battery, expressed in volts (V).
   • $i$ is the current in amperes (A).

2. Derivation of the Formula:

   • Power in an electrical circuit can also be expressed using the formula $P = V \times i$, where $V$ represents voltage.
   • In this case, since the EMF represents the total voltage provided by the battery, we substitute $V$ with $E$, leading to the equation $P = E \times i$.
   • Rearranging gives you the formula $P = \frac{E}{i}$, indicating that as the current increases, the power dissipated will decrease, assuming a constant EMF.

3. Practical Implications:

   • This equation helps in optimizing battery usage in circuits, as it illustrates how the power output can vary with changes in current.
   • Understanding this relationship is crucial when designing circuits that require efficient energy use from a battery.

Conclusion

Thus, the equation $P = \frac{E}{i}$ summarizes how the power dissipated relates to the EMF of the battery and the current flowing through the circuit. The power dissipation is inversely proportional to the current if the EMF remains constant, highlighting important considerations for managing energy in electrical circuits.