27.3:
Resistors In Parallel
In a parallel connection, the circuit elements are connected between the same two terminals.
The advantage of parallel connection is that, even if one element in the circuit breaks, it does not affect the other elements.
Consider three resistors connected directly across the battery of terminals of voltage "V" and current "I".
Since all the resistors are connected between the same terminals, they have the same potential drop.
In contrast, the current through each branch varies depending on the value of the resistor. A high-value resistor will limit more current.
However, the sum of individual currents across each resistor equals the total current drawn from the battery.
The combination of resistors can be treated as equivalent to a single resistor, whose value is always less than the smallest resistance in the circuit.
The ratio of the total current and the potential difference equals one by equivalent resistance.
This expression can be generalized for any number of resistors.
Thus, the inverse of the equivalent resistance is equal to the sum of the inverses of the individual resistances.
27.3:
Resistors In Parallel
Resistors are in parallel when one end of all the resistors are connected to a continuous wire of negligible resistance and the other end of all the resistors are also connected to one another through a continuous wire of negligible resistance. In the case of a parallel configuration, the potential drop across each resistor is the same. Current through each resistor can be found using Ohm’s law, I = V/R, where the voltage is constant across each resistor. The sum of the individual currents equals the current that flows into the parallel connections.
The expression for equivalent resistance can be generalized for the n-number of resistors connected parallelly.
For any number of resistors in parallel, the reciprocal of the equivalent resistance equals the sum of the reciprocals of their individual resistances.
An automobile’s headlights and taillights, radio, and the wiring in a house or any building are examples of systems that are wired in parallel. The advantage of connecting a circuit in parallel combination is that each subsystem utilizes the total voltage of the source and can operate independently. If one component in the parallel circuit burns out, the others keep working.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 10.2; pages 443–444.