Work and performance in direct current circuit
1.State the basic relations for calculating work and power in a direct current circuit.
Solution:
2.The powers of two heating elements are P1 = 18W, P2 = 24W at a voltage U = 12V. What power will both elements have when connected to the same voltage 12V if we connect them:
- a) in parallel
- b) in series
Solution:
Analysis:
P1 = 18W, P2 = 24W, U = 12V, R1 = ?, R2 =?, P = ?, P‘ =?
- When connected in parallel the power will be 42W
- When in series 10.28W.
3.From a nichrome wire (ρ = 0.44·10-6 Ω·m) with diameter d = 0.5 mm a heating coil is to be made, in which at a voltage of 120V 1667 kJ of heat would be generated in 1 hour. What length of wire is required?
Solution:
Analysis:
The length of wire required to make the heating coil is 14 m.
4.An electric heating pad connected to the highest heating level has at voltage U = 220V a power P = 15W. What is the resistance of the pad? What current flows through it? How much electrical energy does it consume in 10 hours of operation?
Solution:
Analysis:
The resistance of the pad is 3.2 kΩ, the current 68 mA and in 10 hours it consumes 0.15 kWh of electrical energy.
5.What ampere fuse should be used to protect an electrical line in which 10 bulbs 100W/220V are connected in parallel at a voltage of 220V.
Solution:
Analysis:
U = 220V, P = 100W, n = 10, I = ?
A 5A fuse should be connected to the electrical line.
6.To a flat battery with Ue = 4.5V and Ri = 1Ω a bulb with resistance R = 9Ω is connected. Determine the total power of the battery Pz, the useful power in the external circuit (power of the bulb P) and the efficiency of energy transfer from the battery to the bulb.
Solution:
Analysis:
Ue = 4.5V, Ri = 1Ω, R = 9Ω, PZ = ?, η = ?
The efficiency of energy transfer from the battery to the bulb is η = 90.
7.What current flows through an electric cooker if 10 liters of water are heated on it from 20°C to 100°C in 30 minutes? The efficiency of the cooker is 75%, the mains voltage is 230V. (c = 4180 J·kg-1·K-1)
Solution:
Analysis:
m = 10 kg, Δt = 80°C = 80 K, U = 230V, τ = 30 min = 1800 s, η = 0.75, c = 4180 J·kg-1·K-1
Approximately 11 A flows through the electric cooker.
8.An elevator with mass 1.2 tons rose to a height of 15 m in 0.5 min. The voltage at the terminals of the motor that lifted the elevator is 230V (η = 90%). Determine the current passing through the meter!
Solution:
Analysis:
m = 1200 kg, t = 30 s, h = 15 m, U = 230V, η = 90% = 0.9, I = ?
The meter current is I = 29 A.
9.Three identical flat batteries are connected in a circuit, each with Ue = 4.5V and Ri = 1.5Ω. The external resistance connected to the circuit is R = 10Ω. Determine the electrical power in the external circuit when the batteries are connected
- a.) in series
- b.) in parallel
Solution:
Analysis:
Ue = 4.5V and Ri = 1.5Ω, R = 10Ω, n = 3, P1 = ?, P2 = ?
- For series connection of the batteries P1 = 8.67W
- for parallel P2 = 1.84W.
10.When a device with R1 = 5Ω is connected to a given source Ue the power of the device is the same as the power of a device with R2 = 0.2Ω connected to the same source. Determine the internal resistance of the source Ri and for each device also its efficiency.
Solution:
Analysis:
R1 = 5Ω, R2 = 0.2Ω, Ri = ?, η1= ?, η2= ?,
