Problem Set 9.1 | Electric Current and Ohm’s Law

Problems

  1. Define electric current, voltage, and resistance in terms of electron flow and energy.

  2. A circuit has a voltage of $230~\mathrm{V}$ (typical European mains) and a current of $1.75~\mathrm{A}$ flowing through it.
    a) Calculate the resistance in the circuit.
    b) Explain why doubling the voltage would double the current.

  3. A $470~\Omega$ resistor is connected to a $9.00~\mathrm{V}$ battery (common for electronics).
    a) What is the current flowing through the circuit?
    b) If the resistor is replaced with a $1.00~\mathrm{k}\Omega$ resistor, how does the current change?

  4. A microwave oven draws $12.5~\mathrm{A}$ of current when connected to a $120~\mathrm{V}$ outlet (typical US mains). What is its resistance?

  5. An LED has a resistance of $33.0~\Omega$ and requires $15.0~\mathrm{mA}$ to operate.
    a) What voltage must be applied across the LED?
    b) Why is the direction of current flow important for LEDs?

  6. A battery supplies $24.0~\mathrm{V}$ to a circuit with two identical resistors. If the total current is $0.800~\mathrm{A}$, what is the resistance of each resistor?

  7. A car battery provides $12.6~\mathrm{V}$. If a car starter motor draws $185~\mathrm{A}$ during starting:
    a) Calculate the resistance of the starter motor.
    b) How much charge flows through it in $3.00~\mathrm{s}$?

  8. A laptop charger supplies $19.5~\mathrm{V}$ and $3.33~\mathrm{A}$ to charge in 2.00 hours.
    a) What is the effective resistance of the charging circuit?
    b) How much charge is transferred in the $2.00~\mathrm{hours}$?


Solutions

  1. Basic Definitions:
    • Current: Flow rate of electric charge
    • Voltage: Electric potential difference driving current
    • Resistance: Opposition to current flow, dissipates energy as heat
  2. a) $R = 131~\Omega$

    b) Doubling voltage doubles current when resistance is constant (Ohm’s Law)

  3. a) $I = 0.0191~\mathrm{A}$

    b) $I = 0.00900~\mathrm{A}$

  4. $R = 9.60~\Omega$

  5. a) $V = 0.495~\mathrm{V}$

    b) LEDs are diodes that only conduct in one direction

  6. If series: $R_{each} = 15.0~\Omega$ If parallel: $R_{each} = 60.0~\Omega$

  7. a) $R = 0.0681~\Omega$

    b) $Q = 555~\mathrm{C}$

  8. a) $R = 5.86~\Omega$

    b) $Q = 24000~\mathrm{C}$