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Difficulty: MediumSeries Circuits

A DC power supply is connected across a series circuit containing two resistive components. Fill in the blanks with the correct numerical values to complete the circuit analysis.

Answer:A 50 V50\text{ V} DC source is connected in series with a 15 Ω15\ \Omega resistor and a second resistor R2R_2. If the circuit draws a current of 2 A2\text{ A}, the total circuit resistance is 【25】 Ω\Omega, and the resistance of R2R_2 is 【10】 Ω\Omega.

Answer

The total circuit resistance is 25 Ω25\ \Omega, and the resistance of R2R_2 is 10 Ω10\ \Omega.
Applying Ohm's Law to the total circuit yields a total resistance of RT=50 V2 A=25 ΩR_T = \frac{50\text{ V}}{2\text{ A}} = 25\ \Omega. In a series circuit, total resistance equals the sum of the individual component resistances (RT=R1+R2R_T = R_1 + R_2). Subtracting the known resistor value (15 Ω15\ \Omega) from the total resistance (25 Ω25\ \Omega) results in R2=10 ΩR_2 = 10\ \Omega.

Step-by-Step Solution

1
Calculate the total circuit resistance (RTR_T) using Ohm's Law with source voltage and total current.
RT=VTI=50 V2 A=25 ΩR_T = \frac{V_T}{I} = \frac{50\text{ V}}{2\text{ A}} = 25\ \Omega
In any complete circuit, the total equivalent resistance equals total source voltage divided by the total circuit current.
2
Calculate the resistance of R2R_2 using the series circuit resistance addition formula (RT=R1+R2R_T = R_1 + R_2).
R2=RT−R1=25 Ω−15 Ω=10 ΩR_2 = R_T - R_1 = 25\ \Omega - 15\ \Omega = 10\ \Omega
In a series circuit, total resistance is the direct sum of individual component resistances.

Key Concept

In a series circuit, total resistance is the direct sum of individual resistances (RT=R1+R2+…R_T = R_1 + R_2 + \dots), and the circuit current is constant through all components as governed by Ohm's Law (RT=VT/IR_T = V_T / I).
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Series Circuits

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