Rechargeable Battery Equations

The rechargeable battery equations found here are used for calculating battery capacity, performance and other characteristics.

Rechargeable Battery Equations: Ohm’s Law

In a given electrical circuit, the amount of current in amperes (I) is equal to the pressure in volts (V) divided by the resistance, in ohms (R). Ohm's law formulas:

To find Current I = V / R

To find Voltage V = I x R

To find Resistance R = V / I

Rechargeable Battery Equations: Calculating Power

Defined by voltage (V) and current (I), Power (P) = VI.

Since V =IR ( Ohm's Law ), P = I² x R and P = V²/ R

Power also can be described by energy emitted per unit of time:

P = E / t.

Thus E = VIt = qV.

This unit of measurement is known typically as a Watt/hr.

Rechargeable Battery Equations: What is C-Rate?

Charge and discharge current of a battery is called C-rate. For example, 1C is the battery capacity for 1 hour fully discharged. A 2400mAh battery has a 1C of 2400mAh.

• 1C from a 1000mAh battery is 1000mAh of current for one hour if discharged at 1C rate.
• 1C is often referred to as a one-hour discharge.
• a 0.5C would be a two-hour, 0.25 C would be for 4 hours.
• a 0.1C a 10-hour discharge.

In other words C-rate X hours = 1C, therefore 0.25C X 4 hours = 1C.

The same equation can be used for high discharge that occurs in less than 1 hour. Let’s assume the following examples for a 2500 mAh battery:

• For this battery is C = 2500 mAh
• At 2C, the battery is delivering 2 X 2500 mA = 5000 mAh.
• Therefore the duration of the 2C discharge is C-rate X time = Capacity, 2C x 0.5h = 2 x 2500 mAh X 0.5h = 2500 mA.
• At 4C, a 1000mAh battery would deliver 4000mA for 15 minutes.

C-Rate Reality

•  C-Rates provided my manufacturers are based on slow discharge of 0.1 to 0.25C.
•  Higher rate discharge results in less total Current being delivered.
•  Higher rate discharge causes internal energy losses and a voltage drop.
•  The battery reaches the low-end voltage cut-off sooner at higher C-rates.