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 r…
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.
View the full transcript and gain access to JoVE Core videos
Q1: What does it mean when resistors are connected in parallel?
Resistors are in parallel when one end of all resistors connects to a continuous wire and the other end connects through another continuous wire of negligible resistance. In this configuration, all resistors share the same two terminals, meaning they experience identical potential drops across them regardless of their individual resistance values.
Q2: How does current distribute across resistors in a parallel circuit?
Current through each resistor varies based on its resistance value, calculated using Ohm's law where I = V/R. Since voltage is constant across all parallel resistors, higher-resistance resistors limit more current while lower-resistance resistors allow more current. The sum of individual currents equals the total current drawn from the battery.
Q3: What is the formula for equivalent resistance in parallel circuits?
For any number of resistors in parallel, the reciprocal of the equivalent resistance equals the sum of the reciprocals of individual resistances: 1/R_eq = 1/R1 + 1/R2 + 1/R3... The equivalent resistance is always less than the smallest individual resistance in the circuit.
Q4: Why is parallel connection advantageous in electrical systems?
Parallel circuits allow each component to operate independently at the full source voltage. If one component fails or burns out, others continue functioning normally. This design principle is used in household wiring and electrical safety systems, where appliances and lights operate independently without affecting each other.
Q5: How does parallel connection differ from series connection in circuits?
In parallel circuits, all resistors connect between the same two terminals with identical potential drops, while current varies per branch. In series circuits, resistors connect end-to-end with the same current flowing through all, but potential drops vary. Parallel configuration offers independent operation; series does not.
Q6: What are real-world examples of parallel circuit applications?
Automobile headlights, taillights, and radios use parallel wiring. Household electrical systems wire outlets, lights, and appliances in parallel so each device operates independently at full voltage. This configuration ensures that turning off one device does not affect others, making it ideal for practical electrical installations.
Q7: How can you calculate current through a specific resistor in parallel?
Use Ohm's law: I = V/R, where V is the constant potential drop across all parallel resistors and R is the individual resistor's resistance. Since voltage is identical across each branch in a parallel circuit, you can directly determine current for any resistor by dividing the voltage by that resistor's resistance value.