DC Electric Circuits

Problem 31: A load of 10 ohms was connected to a 12-volt battery. The current drawn was 1.18 amperes. What is the internal resistance of the battery?

Problem 32: The potential at the terminals of the battery falls from 9 V on open circuit to 6 volts when a resistor of 10 ohms is connected across its terminals. What is the internal resistance of the battery?

Problem 33: The electromotive force of a standard cell is measured with a potentiometer that gives a reading of 1.3562 V. When a 1.0 megaohm resistor is connected across the standard cell terminals, the potentiometer reading drops to 1.3560 V. What is the internal resistance of the standard cell?

Problem 34: A battery is formed of five cells joined in series. When the external resistance is 4 ohms, the current is 1.5 A and when the external resistance is 9 ohms, the current falls to 0.75 A. Find the internal resistance of each cell.

Problem 35: A Barangay power station supplies 60 kW to a load over 2,500 ft, 100 mm² two-conductor copper feeder, the resistance of which is 0.078 ohm per 1000 ft. The bus bar voltage is maintained constant at 600 V. Determine the load current.

Problem 36: A 120 V DC motor draws current of 100 A and is located 1000 ft from the supply source. If the diameter of the copper transmission line is 0.45 inch, what must be the voltage of the supply?

Problem 37: A LRT car, 5 km distance from the Tayuman, takes 100 A over a 100 mm² hard drawn copper trolley wire having a resistance of 0.270 ohm per km. The rail and ground return has a resistance of 0.06 ohm per km. If the station voltage is 750 V, what is the voltage of the car?

Problem 38: The hot resistance of an incandescent lamp is 10 ohms and the rated voltage is 50 V. Find the series resistance required to operate the lamp from an 80 V supply.

Problem 39: A resistive coil draws 2 A at 110 V after operating for a long time. If the temperature rise is 55°C above the ambient temperature of 20°C, calculate the external resistance which must be initially connected in series with the coil to limit the current to 2 A. The temperature coefficient of the material of the coil is 0.0043 per °C at 20°C.

Problem 40: A carbon resistor dissipates 60 W of power from a 120 V source at 20°C. How much power will be dissipated in the resistor at 120°C if connected across the same source? Assume the temperature coefficient of carbon at 20°C is -0.0005 per °C.

Problem 41: Two (2) 115-V incandescent lamps A and B are connected in series across a 230-V source. If lamp A is rated 75 watts and lamp B is rated 50 watts, determine the current drawn by the series connection.

Problem 42: An arc lamp takes 10 A at 50 volts. A resistance R is to be place in series so that the lamp may burn correctly from a 110 V supply. Find the power wasted in this resistor.

Problem 43: Conductor 'x' of a certain material and a given cross section has a resistance of 0.1 ohm per meter and a temperature coefficient of 0.005 per °C. Conductor 'y' of another material and a given cross section has a resistance of 0.5 ohms per meter and a temperature coefficient of 0.001 per °C. It is desired to make a coil having a resistance of 500 ohms and a temperature coefficient of 0.002 by using suitable lengths of the two wires connected in series. Calculate the required length of wire 'x'.

Problem 44: If a resistor rated at 5 watts and 6 volts are connected across a battery with an open circuit voltage of 6 volts. What is the internal resistance of the battery if the resulting current is 0.8 A?

Problem 45: A high voltage DC transmission line delivers 1000 MW at 500 kV to an aggregate load over a distance of 900 km. Determine the voltage at the sending end. Assume the loop resistance of the line to be 1 mΩ per km.

Problem 46: It is required that a loading of 3 kW be maintained in a heating element at an initial temperature of 20°C, a voltage of 220 V is necessary for the purpose. After the element has settled down to steady state, it is found that a voltage of 240 volts is necessary to maintain the 3 kW loading. The element resistance temperature coefficient is 0.0006 per degree centigrade at 20°C. Calculate the final temperature of heating element.

Problem 47: A 200-W, 110-V incandescent lamp has a filament having a temperature coefficient of resistance equal to 0.005 at 0°C. If the normal operating temperature of the bulb is 2500°C, how much current will the bulb draw at the instant it is turned on. Assume a room temperature of 20°C.

Problem 48: The power drawn by a resistive coil made of copper wire is 220 W at 100 V and 20°C. Calculate the power consume by the coil at 115 V and 100 °C. The temperature coefficient of resistance at 20°C is 0.00393.

Problem 49: An electric water heater has a rating of 1 kW, 230 V. The coil used as the heating element is 10 m long and has a resistivity of 1.724 x 10⁻⁶ ohm-cm. Determine the required diameter of the wire in mils.

Problem 50: When two resistors A and B are connected in series, the total resistance is 36 ohms. When connected in parallel, the total resistance is 8 ohms. What is the ratio of the resistance Ra to resistance Rb. Assume Ra < Rb.