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A circuit is the route electricity follows from where it is generated to where it is used.

Photovoltaic solar cells use circuits too. Sunlight hits a panel and triggers the electrons to move through the cell. A wire leaves the cell, continuing the circuit and after it passes through the appliance (a lightbulb), the circuit moves back to the solar cell.
Let's say that you want to use the microwave oven. The electricity is routed through your home's fuse box. You push the start button on the microwave and you "close" a circuit — loop for electrons to flow through. Electricity now flows through a loop of wires from the electrical line outside of your home to the microwave oven. When the food is cooked and you turn the microwave off, the circuit is "opened". No electricity flows to the microwave. That doesn't mean there isn't electricity in the wires. If you cut into the cord with a pair of scissors, you would be in for a deadly surprise. You would close the circuit, but now the electrons would flow through you. Ouch.

The following diagram shows the circuit between a battery and a lightbulb.

 
electrical circuit The battery is the source of power. Electrons (electricity) flow along the wire. The electricity goes through a lightswitch. Inside the switch is a fuse that breaks the circuit. When the switch is in the off position, the electricity cannot travel through the wire. It is blocked. When the switch is in the on position, the electricity can travel through the restored circuit and make it to the lightbulb.

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