Circuit Elements and Ohm’s Law (4C) - Chem & Physics

1. Identify the equivalent resistance of three identical resistors $R$ connected in parallel.

   $R_{\text{eq}} = \frac{R}{3}$. For identical parallel resistors, equivalent resistance equals individual resistance divided by the number.

2. Find the power dissipated by a $6\,\Omega$ resistor with a $12\,\text{V}$ drop across it.

   $P = 24\,\text{W}$. Power dissipation is voltage squared divided by resistance.

3. What circuit quantity is the same through all elements in a series connection?

   Current $I$ is the same through each series element. In series circuits, conservation of charge ensures identical current through all elements.

4. State Kirchhoff's voltage law (KVL) for a closed loop in a circuit.

   $\sum \Delta V = 0$ around any closed loop. Kirchhoff's voltage law upholds energy conservation, summing potential differences to zero in a closed loop.

5. State the power dissipated by a resistor in terms of voltage and resistance.

   $P = \frac{V^2}{R}$. Power in a resistor also derives from Ohm's law, expressed as voltage squared divided by resistance.

6. Find the equivalent resistance of $2\,\Omega$ and $3\,\Omega$ connected in series.

   $R_{\text{eq}} = 5\,\Omega$. Equivalent resistance in series is the sum of individual resistances.

7. What is the SI unit of electric potential difference (voltage), expressed using base SI units?

   Volt (V); $1\,\text{V} = 1\,\text{J}\,\text{C}^{-1}$. Voltage represents the potential energy difference per unit charge, equivalent to one joule per coulomb.

8. State the formula for equivalent resistance of resistors in parallel.

   $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$. In parallel, reciprocals of resistances add due to increased conductance from multiple paths.

9. State the formula for Ohm's law relating voltage, current, and resistance.

   $V = IR$. Ohm's law states that potential difference is directly proportional to current, with resistance as the proportionality constant.

10. State the formula for equivalent resistance of resistors in series.

    $R_{\text{eq}} = R_1 + R_2 + \cdots$. In series, resistances add because the same current flows through each, accumulating opposition.

11. What is the SI unit of electric current, and what does it represent in terms of charge flow?

    Ampere (A); $1\,\text{A} = 1\,\text{C}\,\text{s}^{-1}$. Electric current measures the rate of charge flow, defined as one coulomb per second in SI units.

12. State the formula for electrical energy transferred over time by a circuit element.

    $E = Pt$. Electrical energy is the product of power and time for constant power dissipation.

13. What is the definition of an ohmic device in terms of the $I$-$V$ relationship?

    It has constant $R$; $I \propto V$ (linear $I$-$V$ curve). An ohmic device obeys Ohm's law with constant resistance, yielding a linear current-voltage relationship.

14. Find the voltage drop across a $5\,\Omega$ resistor carrying $2\,\text{A}$ of current.

    $V = 10\,\text{V}$. Ohm's law calculates voltage as current multiplied by resistance.

15. State the power dissipated by a resistor in terms of current and resistance.

    $P = I^2R$. For resistors, power dissipation derives from combining Ohm's law with the general power formula, using current squared times resistance.

16. State the formula for electrical power dissipated by a circuit element in terms of $I$ and $V$.

    $P = IV$. Electrical power is the rate of energy transfer, given by the product of current and voltage.

17. What circuit quantity is the same across all branches in a parallel connection?

    Voltage $V$ is the same across each parallel branch. In parallel circuits, branches share the same potential difference due to common connection points.

18. What is the relationship between resistance, resistivity, length, and cross-sectional area?

    $R = \rho\frac{L}{A}$. Resistance scales with material resistivity and length while inversely with cross-sectional area.

19. State Kirchhoff's current law (KCL) for a node in a circuit.

    $\sum I_{\text{in}} = \sum I_{\text{out}}$. Kirchhoff's current law enforces charge conservation at a node, balancing incoming and outgoing currents.

20. If wire cross-sectional area $A$ doubles (same $\rho$ and $L$), how does resistance change?

    $R$ halves: $R \propto \frac{1}{A}$. Resistance is inversely proportional to cross-sectional area, so doubling area halves resistance.

21. Find the current when a $12\,\text{V}$ battery is connected to a $3\,\Omega$ resistor.

    $I = 4\,\text{A}$. Ohm's law gives current as voltage divided by resistance.

22. Find the equivalent resistance of $2\,\Omega$ and $3\,\Omega$ connected in parallel.

    $R_{\text{eq}} = \frac{6}{5}\,\Omega$. Equivalent resistance in parallel is the reciprocal of the sum of reciprocals.

23. What is the SI unit of resistance, expressed using volts and amperes?

    Ohm ($\Omega$); $1\,\Omega = 1\,\text{V}\,\text{A}^{-1}$. Resistance quantifies opposition to current flow, defined as one volt per ampere.

24. If wire length $L$ doubles (same $\rho$ and $A$), how does resistance change?

    $R$ doubles: $R \propto L$. Resistance is directly proportional to length, so doubling length doubles resistance.

25. Find the power dissipated by a $4\,\Omega$ resistor when the current is $3\,\text{A}$.

    $P = 36\,\text{W}$. Power dissipation uses current squared multiplied by resistance.

Study these flashcards