Practice Problems: DC Circuits
Question 1
A power systems engineer is analyzing a distribution network supplying a remote industrial facility. The facility is located 2000 feet from the main substation and is connected via copper conductors. The facility draws a steady-state current of 150 A at 480 V DC. The conductor has a resistance of 0.08 Ω per 1000 feet. What is the voltage drop across the transmission line (round trip)?
(a) 24 V
(b) 36 V
(c) 48 V
(d) 12 V
Question 2
An electrical engineer is designing a backup power system for a telecommunications facility. The system uses a 48 V DC battery bank that must supply power to equipment drawing 75 A continuously for 4 hours during an outage. The batteries have an internal resistance of 0.05 Ω. What is the total energy dissipated as heat in the internal resistance during the 4-hour period?
(a) 4.05 kWh
(b) 1.125 kWh
(c) 2.25 kWh
(d) 0.563 kWh
Question 3
A control systems engineer is troubleshooting a circuit with three resistors in series: R₁ = 220 Ω, R₂ = 470 Ω, and R₃ = 330 Ω. The circuit is powered by a 24 V DC source. A multimeter reading shows that the voltage across R₂ is 11.04 V. What is the current flowing through the circuit?
(a) 23.5 mA
(b) 20.0 mA
(c) 25.5 mA
(d) 18.8 mA
Question 4
A facilities engineer is analyzing the power distribution in a data center. A 120 V DC bus supplies three parallel loads: Load 1 draws 15 A, Load 2 draws 22 A, and Load 3 draws 18 A. The bus has a source resistance of 0.08 Ω. What is the actual terminal voltage at the load connection point?
(a) 115.6 V
(b) 118.2 V
(c) 119.4 V
(d) 116.8 V
Question 5
An automotive engineer is designing a battery monitoring system for an electric vehicle. The system has a 400 V battery pack with an internal resistance of 0.12 Ω. During regenerative braking, the charging current is 85 A. What is the actual voltage across the battery terminals during this charging process?
(a) 389.8 V
(b) 410.2 V
(c) 400.0 V
(d) 395.5 V
Question 6
A power engineer is designing a current divider circuit for a sensing application. The circuit has two parallel branches: R₁ = 680 Ω and R₂ = 820 Ω. The total current entering the parallel combination is 45 mA. What is the current through R₁?
(a) 24.6 mA
(b) 22.3 mA
(c) 20.4 mA
(d) 26.8 mA
Question 7
A test engineer is calibrating equipment using a Wheatstone bridge circuit. The bridge has three known resistances: R₁ = 1000 Ω, R₂ = 2200 Ω, and R₃ = 1500 Ω. The bridge is balanced (zero galvanometer reading). What is the value of the unknown resistance R₄?
(a) 3300 Ω
(b) 2750 Ω
(c) 3000 Ω
(d) 2500 Ω
Question 8
A telecommunications engineer is designing a DC power system for a cell tower. The system uses three 12 V batteries connected in series to create a 36 V supply. Each battery has an internal resistance of 0.04 Ω. When supplying a load, the terminal voltage measures 34.2 V. What is the load current?
(a) 15.0 A
(b) 12.5 A
(c) 18.0 A
(d) 10.0 A
Question 9
An instrumentation engineer is analyzing a voltage divider circuit used for signal conditioning. The divider consists of R₁ = 10 kΩ connected to the positive supply and R₂ = 15 kΩ connected to ground. The supply voltage is 25 V. A load of 30 kΩ is connected across R₂. What is the loaded output voltage?
(a) 12.5 V
(b) 10.0 V
(c) 11.1 V
(d) 13.3 V
Question 10
A maintenance engineer is testing a DC motor drive circuit. The circuit contains a series combination of a 5 Ω resistor and a motor with 3 Ω resistance. A parallel branch contains a 12 Ω resistor. The entire circuit is powered by a 48 V source. What is the total power dissipated in the circuit?
(a) 288 W
(b) 336 W
(c) 384 W
(d) 240 W
Question 11
A solar installation engineer is designing a photovoltaic array connection system. Four identical solar panels are connected in a series-parallel configuration: two series strings of two panels each, connected in parallel. Each panel produces 36 V and 8 A under standard conditions. What is the total power output of the array?
(a) 2304 W
(b) 1152 W
(c) 4608 W
(d) 576 W
Question 11 (Corrected)
A solar installation engineer is designing a photovoltaic array connection system. Four identical solar panels are connected in a series-parallel configuration: two series strings of two panels each, connected in parallel. Each panel produces 36 V and 8 A under standard conditions. What is the total power output of the array?
(a) 1152 W
(b) 2304 W
(c) 576 W
(d) 4608 W
Question 12
A design engineer is specifying wire gauge for a 125 A DC welding system. The wire run is 50 feet one-way (100 feet round trip). The maximum allowable voltage drop is 3% of the 230 V supply voltage. What is the maximum wire resistance per 1000 feet that can be used?
(a) 0.552 Ω/1000 ft
(b) 0.690 Ω/1000 ft
(c) 0.460 Ω/1000 ft
(d) 0.345 Ω/1000 ft
Question 13
A circuit designer is analyzing a complex resistor network. Three resistors are connected as follows: R₁ = 24 Ω and R₂ = 36 Ω are in series, and this combination is in parallel with R₃ = 40 Ω. A 120 V source is connected across the entire combination. What is the current through R₃?
(a) 3.0 A
(b) 2.4 A
(c) 4.0 A
(d) 2.0 A
Question 14
A power quality engineer is measuring the efficiency of a DC-DC converter system. The input voltage is 48 V with an input current of 12.5 A. The output voltage is 24 V with an output current of 23.5 A. What is the efficiency of the converter?
(a) 94.0%
(b) 89.5%
(c) 91.2%
(d) 96.8%
Question 15
An electrical engineer is designing a battery discharge test circuit. A 12 V battery with 0.08 Ω internal resistance is connected to a variable load. The engineer needs to extract maximum power from the battery. What load resistance should be used, and what is the maximum power delivered to the load?
(a) RL = 0.08 Ω, Pmax = 450 W
(b) RL = 0.08 Ω, Pmax = 225 W
(c) RL = 0.16 Ω, Pmax = 450 W
(d) RL = 0.04 Ω, Pmax = 300 W
Question 16
A test engineer is using Thévenin's theorem to simplify a circuit for analysis. The original circuit has an open-circuit voltage of 18 V measured at the terminals. When a 6 Ω load is connected, the terminal voltage drops to 12 V. What is the Thévenin equivalent resistance of the circuit?
(a) 3 Ω
(b) 4 Ω
(c) 2 Ω
(d) 6 Ω
Question 17
A controls engineer is designing a sensor circuit using a bridge configuration. The circuit has a 24 V supply and four arms with resistances: R₁ = 500 Ω, R₂ = 500 Ω, R₃ = 480 Ω (sensor), and R₄ = 520 Ω. What is the voltage difference between the two bridge output terminals?
(a) 0.48 V
(b) 0.96 V
(c) 0.24 V
(d) 1.20 V
Question 18
A reliability engineer is analyzing the failure mode of a redundant power supply system. Two identical 48 V DC power supplies, each capable of delivering 30 A, are connected in parallel to share the load. Due to a fault, one supply develops an internal series resistance of 0.15 Ω while the other remains at 0.05 Ω. If the load draws 40 A total, what current does the faulty supply provide?
(a) 10 A
(b) 15 A
(c) 20 A
(d) 12 A
Question 19
A facilities engineer is calculating the operating cost of a DC electric heating system in an industrial process. The heater consists of three 15 Ω heating elements connected in parallel, operating from a 240 V DC supply for 16 hours per day. Electricity costs $0.12 per kWh. What is the monthly operating cost (30 days)?
(a) $1,382.40
(b) $1,843.20
(c) $2,073.60
(d) $1,152.00
Question 19 (Corrected)
A facilities engineer is calculating the operating cost of a DC electric heating system in an industrial process. The heater consists of three 15 Ω heating elements connected in parallel, operating from a 240 V DC supply for 16 hours per day. Electricity costs $0.12 per kWh. What is the monthly operating cost (30 days)?
(a) $663.55
(b) $1,382.40
(c) $884.74
(d) $552.96
Question 20
A design engineer is specifying a current sensing resistor (shunt) for a 200 A DC circuit. The measurement system requires a 100 mV signal at full-scale current. The shunt must dissipate the power as heat. What is the power dissipation in the shunt resistor at full-scale current?
(a) 20 W
(b) 15 W
(c) 25 W
(d) 10 W
