Exam 18: Electric Current and Circuits

A capacitor in an RC circuit is charged, storing 1.25 mJ of energy. What is the time required to discharge this capacitor (say, to 1% of its initial charge), as compared to the time required to discharge (to 1%) an identical capacitor in an identical RC circuit which has stored 2.5 mJ of energy instead?

A resistor has a resistance of 30 Ω at 20°C. If the temperature coefficient of resistivity is 4.5 × 10⁻³ °C⁻¹, what is its resistance at 200°C?

A 6.0 Ω resistor and a 3.0 Ω resistor are connected in series to a 1.5 V battery of negligible internal resistance. What is the current in the 3.0 Ω resistor?

Two identical circuits have a capacitor in series with a resistor and a switch. In circuit A, the resistor has resistance R, while in circuit B, its resistance is 4R. The capacitors are identical. Each capacitor begins fully charged, and each circuit is open. When each circuit is completed (i.e., the switch in them is closed), the capacitor will begin to discharge. If a time t is required for circuit A's capacitor to fully discharge (say, by 99%), what time will be required for circuit B's capacitor to do the same?

Three resistors, R₁ = 4.0 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the total power dissipated by the circuit?

Three resistors, R₁ = 9.00 Ω, R₂ = 3.00 Ω, and R₃ = 1.00 Ω, are connected in parallel to a 9.00 V battery. What is the total power dissipated in the circuit?

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-half its maximum value?

A flashlight, which uses two 1.5 V batteries in series, is turned on for 2.0 minutes. If the current in the flashlight is 100 mA, what is the energy dissipated?

A 1000 Ω resistor is in a circuit with 30.0 mA flowing through it. A voltmeter with internal resistance 1000 Ω is used to measure the voltage across the resistor. What is the reading on the voltmeter if a total current of 30.0 mA still flows in the circuit?

A carbon resistor is made of a cylinder of carbon, of diameter 7.4 mm. If the resistivity of carbon is 3.5 × 10⁻⁵ W·m, and a potential difference of 0.15 V causes a current of 12 A to flow through the resistor, what is the length of the cylinder?

A three-cell flashlight has 3 batteries in series, each with an emf of 1.5 V. If the bulb has a resistance of 50 Ω, what current flows when the flashlight is operating? (Assume the internal resistance of the batteries is negligible.)

In the diagram, if the current through R₁ is 5 A up, and the current through R₃ is 3 A up, what is the current in R₂?

A wire of radius 0.15 mm is made of an unknown metal and carries a current of 8.4 mA. The drift velocity for electrons in the wire is measured to be 36 × 10⁻⁶ m/s. What is the charge carrier density of the metal from which the wire is made?

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. What is the time constant for this circuit?

Copper has 8.5 × 10²⁸ current carrying electrons per m³. A copper wire carries a current of 17 mA, and the drift velocity of the electrons is measured to be 18 × 10⁻⁶ m/s. What is the wire's radius?

A bird can safely land on a bare, high-voltage power line because

A 12.0 V battery has an internal resistance of 0.080 Ω. If the battery supplies 100 A when connected to a starter motor, what is the resistance of the motor?

Two capacitors of values 6.0 mF and 9.0 mF are connected in series to a 30.0 V power supply. What is the resulting potential difference across the 6.0 mF capacitor?

An electron beam contains 1.5 × 10¹⁷ electrons per m³ and is confined to circular cross-sectional region of diameter 0.025 mm. The electrons in the beam are extremely energetic and travel at nearly the speed of light. What is the current in the beam?

Two carbon cylinders have radii 2r and r, and the first has length 2L, while the second has length L. What is the resistance of the first if the resistance of the second is 12 Ω?