Analyzing How Changes in Resistance Affect Circuit Quantities

Q16. For the circuit shown in Fig. 19-38, use the words “increases,” “decreases,” or “stays the same” to complete the following statements:

• a. If $R_7$ increases, the potential difference between A and E (assume no resistance in @ and é).

• b. If $R_7$ increases, the potential difference between A and E (assume @ and & have resistance).

• c. If $R_7$ increases, the voltage drop across $R_a$.

• d. If $R_z$ decreases, the current through $R_1$.

• e. If $R_y$ decreases, the current through $R_e$.

• f. If $R_o$ decreases, the current through $R_3$.

• g. If $R_s$ increases, the voltage drop across $R_z$.

• h. If $R_s$ increases, the voltage drop across $R_a$.

• i. If $R_o$, $R_s$, and $R_7$ increase, ($r = 0$).

Background

Topic: Electric Circuits – Series and Parallel Resistors, Ohm’s Law, and Voltage Division

This question tests your understanding of how changing the value of a resistor in a circuit affects voltages and currents elsewhere in the circuit. You’ll need to apply concepts such as equivalent resistance, Ohm’s Law, and the rules for voltage and current in series and parallel circuits.

Key Terms and Formulas

• Ohm’s Law: $V = IR$

• Series Resistance: $R_{eq} = R_1 + R_2 + \ldots$

• Parallel Resistance: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots$

• Voltage Divider Rule (for series): $V_x = V_{total} \frac{R_x}{R_{total}}$

• Current Divider Rule (for parallel): $I_x = I_{total} \frac{R_{other}}{R_{total}}$

Step-by-Step Guidance

1. For each part, identify whether the resistors in question are in series or parallel, and how changing one resistor affects the total or branch resistance.

2. Recall that increasing resistance in a branch will decrease the current through that branch (by Ohm’s Law), and may affect the voltage across other elements depending on the circuit configuration.

3. For voltage differences (potential differences), use the voltage divider rule if the resistors are in series, or consider how the total current changes if the resistors are in parallel.

4. For current through a resistor, use Ohm’s Law and consider how the total or branch resistance changes when a resistor is increased or decreased.

5. For each statement, reason through the effect of the change (increase or decrease in resistance) on the quantity asked (voltage or current), but stop before stating the final outcome for each part.

Try solving on your own before revealing the answer!