How should two 12-volt 7 amp hour batteries be connected for a 12-volt security system requiring a minimum of 10 Amp Hour of battery capacity?

Connecting the two 12-volt 7 amp hour batteries in parallel is the correct choice, as this configuration effectively combines the capacities of both batteries while maintaining a 12-volt output.

When batteries are connected in parallel, the voltage remains the same as a single battery (12 volts), but the amp hour capacity is additive. Therefore, two 7 amp hour batteries in parallel will provide a total capacity of 14 amp hours. This is more than sufficient for the minimum requirement of 10 amp hours for the security system, ensuring extended operation time before needing a recharge.

In contrast, connecting them in series would double the voltage to 24 volts but would still result in a total capacity of just 7 amp hours, which does not meet the required capacity for the system. Other configurations mentioned would not work for maintaining the desired voltage and capacity or might introduce unnecessary complexity or instability to the power supply system.