Electric Circuits: Series Voltage, Parallel Voltage & Open Circuits

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In electric circuits, when a battery is connected in series with two resistors, and one of those resistors continues in parallel, the voltage across the series resistor can be determined by first simplifying the circuit. This involves calculating the equivalent resistance of the parallel components, which can then be treated as a single resistor in series with the remaining elements. In a series-parallel circuit, the presence of an open circuit affects the overall resistance and voltage distribution. If two resistors are connected in parallel and one is open, only the two closed resistors contribute to the circuit, effectively removing the open resistor from the circuit. The voltage drop across the remaining resistors can then be calculated based on their equivalent resistance. Simplifying the circuit step-by-step by combining parallel and series elements is essential for accurate analysis.
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In electric circuits, you know how parallel voltage is the same throughout, but series voltage adds up to the supply.

What if there is a battery connected in series to two resistors. However, what if one of the resistors continues on parallel. How, then would u find the volts of the solo one in series.

Also, what part does an open circuit play in a parallel circuit. In other words, if the first two resistors connected parallel are closed, but the third is open, what is the result?
 
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I believe that you are asking about a series parallel circuit. These consist of both series and parallel elements. The general scheme is to simplify the circuit by computing the resistance contribution of each simpler portion. When elements are connected in parallel you can compute a single resistance, which will be in series with other elements.

The exact steps needed to simplify a circuit are determined by the circuit so it is difficult to specify a sequence. Start by combining all obvious sections, a pair of resistors in parallel, a leg of series resistors. Once the obvious simplifications are made, redraw the circuit with the simplified representations. Repeat. Repeat the process until you arrive at a single total resistance.

Once you have reduced a parallel set to a single resistance its voltage drop can be computed as if it were a single series resistor.

The result of the single open resistor in a 3 resistor parallel network would be that you have 2 resistor in parallel, the 3rd would not be in the circuit.
 
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