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Difficulty: EasySeries Circuits

Complete the statement describing how adding components affects a series circuit connected to a constant voltage source.

Answer:When an additional resistor is added in series to a circuit connected to a constant voltage source, the total circuit resistance will 【increase】 and the total current in the circuit will 【decrease】.

Answer

increase (for total resistance) and decrease (for total current)
In a series circuit, all components share a single continuous path. The total equivalent resistance is the arithmetic sum of each individual resistance (RT=R1+R2+R3R_T = R_1 + R_2 + R_3). Inserting an additional resistor increases the total circuit resistance. By Ohm's Law (I=VRTI = \frac{V}{R_T}), an increase in total resistance with an unchanging source voltage results in a decrease in total current.

Step-by-Step Solution

1
Determine the effect of adding a resistor on total series resistance.
Total resistance increases.
In a series circuit, total resistance is the sum of all individual resistances (RT=R1+R2+⋯+RnR_T = R_1 + R_2 + \dots + R_n), so adding another resistor always increases the total resistance.
2
Apply Ohm's Law to find the effect on total loop current with a fixed voltage source.
Total circuit current decreases.
According to Ohm's Law (I=VRTI = \frac{V}{R_T}), when source voltage VV remains constant and total resistance RTR_T increases, the total current II must decrease.

Key Concept

Series Resistance and Current Relationship

Alternative Method

Consider a numerical example: a 12 V12\text{ V} source with a single 6 Ω6\ \Omega resistor yields I=12 V6 Ω=2 AI = \frac{12\text{ V}}{6\ \Omega} = 2\text{ A}. Adding another 6 Ω6\ \Omega resistor in series makes RT=12 ΩR_T = 12\ \Omega, which drops current to I=12 V12 Ω=1 AI = \frac{12\text{ V}}{12\ \Omega} = 1\text{ A}.
Estimated Time:45s
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Topics

Series Circuits

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