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Difficulty: MediumSeries Circuits

An industrial direct-current (DC) sensor loop is powered by a 50 V50\text{ V} power source. The loop consists of two series-connected components: a fixed resistor R1=10 ΩR_1 = 10\ \Omega and an unknown resistor R2R_2. An ammeter placed in the circuit measures a continuous current of 2 A2\text{ A}. What is the resistance of R2R_2, and what is the voltage drop across R2R_2?

Answer:The resistance of R2R_2 is 【15】 Ω\Omega, and the voltage drop across R2R_2 is 【30】 V\text{V}.

Answer

The resistance of R2R_2 is 15 Ω15\ \Omega, and the voltage drop across R2R_2 is 30 V30\text{ V}.
In a series circuit, the total resistance is calculated as Rtotal=VtotalI=50 V2 A=25 ΩR_{\text{total}} = \frac{V_{\text{total}}}{I} = \frac{50\text{ V}}{2\text{ A}} = 25\ \Omega. Since Rtotal=R1+R2R_{\text{total}} = R_1 + R_2, the unknown resistance is R2=25 Ω−10 Ω=15 ΩR_2 = 25\ \Omega - 10\ \Omega = 15\ \Omega. The voltage drop across R2R_2 is found by multiplying the common series current by R2R_2, yielding V2=2 A×15 Ω=30 VV_2 = 2\text{ A} \times 15\ \Omega = 30\text{ V} (which also satisfies Kirchhoff's Voltage Law: 50 V−20 V=30 V50\text{ V} - 20\text{ V} = 30\text{ V}).

Step-by-Step Solution

1
Calculate the total equivalent resistance (RtotalR_{\text{total}}) of the series circuit using Ohm's Law.
Rtotal=VtotalI=50 V2 A=25 ΩR_{\text{total}} = \frac{V_{\text{total}}}{I} = \frac{50\text{ V}}{2\text{ A}} = 25\ \Omega
In a closed DC loop, total resistance equals total source voltage divided by total current.
2
Determine the value of the unknown resistor R2R_2 using the series resistance rule.
R2=Rtotal−R1=25 Ω−10 Ω=15 ΩR_2 = R_{\text{total}} - R_1 = 25\ \Omega - 10\ \Omega = 15\ \Omega
Total resistance in a series circuit is the sum of individual resistances (Rtotal=R1+R2R_{\text{total}} = R_1 + R_2).
3
Calculate the individual voltage drop across R2R_2 (V2V_2).
V2=I×R2=2 A×15 Ω=30 VV_2 = I \times R_2 = 2\text{ A} \times 15\ \Omega = 30\text{ V}
The same current flows through all series components; voltage drop across any component equals current multiplied by its resistance (or Vtotal−V1=50 V−20 V=30 VV_{\text{total}} - V_1 = 50\text{ V} - 20\text{ V} = 30\text{ V}).

Key Concept

Series Circuit Resistance and Voltage Division
Estimated Time:1m 0s
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Topics

Series Circuits

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