Question

You make a parallel combination of resistors consisting of resistor A having a very large resistance and resistor B having a very small resistance. The equivalent resistance for this combination will be: a) slightly greater than the resistance of the resistor A. b) slightly less than the resistance of the resistor $\mathrm{A}$. c) slightly greater than the resistance of the resistor B. d) slightly less than the resistance of the resistor B.

Name: Problem 2, Chapter 25: University Physics with Modern Physics
Uploaded: 2021-06-21T17:25:28-08:00
Duration: 1 min 51 s
Channel: Vishal Gupta

   You make a parallel combination of resistors consisting of resistor A having a very large resistance and resistor B having a very small resistance. The equivalent resistance for this combination will be:
a) slightly greater than the resistance of the resistor A.
b) slightly less than the resistance of the resistor $\mathrm{A}$.
c) slightly greater than the resistance of the resistor B.
d) slightly less than the resistance of the resistor B.

University Physics with Modern Physics

Wolfgang Bauer, Gary… 1st Edition

Chapter 25, Problem 2

Instant Answer

Solved by Expert Vishal Gupta

06/21/2021

Step 1

The formula is given by: \[ \frac{1}{R_{eq}} = \frac{1}{R_A} + \frac{1}{R_B} \] Show more…

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You make a parallel combination of resistors consisting of resistor A having a very large resistance and resistor B having a very small resistance. The equivalent resistance for this combination will be: a) slightly greater than the resistance of the resistor A. b) slightly less than the resistance of the resistor $\mathrm{A}$. c) slightly greater than the resistance of the resistor B. d) slightly less than the resistance of the resistor B.

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Key Concepts

Parallel Circuits

In a parallel circuit, all components are connected across the same two nodes, meaning each component experiences the same voltage. This configuration allows current to split among the different branches based on their resistances.

Equivalent Resistance in Parallel

The equivalent resistance of a parallel combination can be determined by the reciprocal formula: 1/Req = 1/R1 + 1/R2 + ... + 1/Rn. This means that the overall resistance is lower than the smallest individual resistor in the network, as the current has multiple paths to follow.

Dominance of the Smallest Resistor

When resistors of vastly different values are arranged in parallel, the smallest resistor largely dictates the overall behavior of the circuit. This is because its low resistance provides an easier path for the current, resulting in an equivalent resistance that is only slightly less than the value of the smallest resistor.

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