Question

a battery for a proposed electric car is to have three hundred 3 - v lithium ion cells connected such that the total voltage across all of the cells is 300 v.

Explanation:

Step1: Calculate voltage of 100 - cell series - connection

When cells are connected in series, the total voltage is the sum of the voltages of individual cells. Each cell has a voltage of 3 V. For 100 cells connected in series, the total voltage $V_{100 - series}=3\times100 = 300$ V.

Step2: Analyze the three - set connection

We have three sets of 100 - cell series - connected batteries. Each set has a voltage of 300 V.

Step3: Determine the connection type and final voltage

These three sets need to be connected in parallel to get a total voltage of 300 V (because in a parallel - connection of voltage - sources, the potential difference across the combination is equal to the potential difference of each source).

Answer:

Take 100 of the batteries and connect them in series, which would give a total voltage of 300 volts. Do that again with the next 100 batteries, and again with the last 100 batteries. That gives 3 sets, each with a total voltage of 300 volts. Then those 3 sets can be connected in parallel with each other. The total combination of batteries would have a potential difference of 300 volts.