Based on the image you uploaded, let’s analyze the questions and solve them step by step:

Question 1:

Parallel resistor circuit with $R_1 = 4\ \Omega$ and $R_2 = 12\ \Omega$, and voltage $V = 3\ \text{V}$.

• Equivalent resistance for parallel resistors: $\frac{1}{R_\text{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ $\frac{1}{R_\text{eq}} = \frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$ $R_\text{eq} = 3\ \Omega$

• Using Ohm's Law, $I = \frac{V}{R_\text{eq}}$: $I = \frac{3}{3} = 1\ \text{A}$

Answer: D. $1\ \text{A}$.

Question 2:

Factors influencing the resistance of a wire:

• Resistance of a wire is given by: $R = \rho \frac{L}{A}$ where $R$ is resistance, $\rho$ is resistivity (depends on the material), $L$ is the length, and $A$ is the cross-sectional area.
• Factors:
  1. Length ($L$) → Directly proportional.
  2. Resistivity of the material ($\rho$) → Depends on the material.
  3. Cross-sectional area ($A$) → Inversely proportional.

Correct Answer: A. (1), (2), and (3).

Question 3:

Three resistors in a series configuration:

• $R_1 = 5\ \Omega, R_2 = 6\ \Omega, R_3 = 3\ \Omega$.
• Total resistance for series: $R_\text{total} = R_1 + R_2 + R_3 = 5 + 6 + 3 = 14\ \Omega$

Answer: C. $14\ \Omega$.

Question 4:

Increasing resistance of a conductor:

• Resistance increases when:
  1. Length ($L$) increases.
  2. Resistivity ($\rho$) increases.
  3. Cross-sectional area ($A$) decreases.

Correct Answer: B. (1) and (2) are increased, (3) is decreased.

Let me know if you need additional details or further clarifications!
Here are five related questions for practice:

1. What is the formula for combining resistors in parallel and in series?
2. How does the resistance change if the length of a wire doubles while its cross-sectional area remains constant?
3. Derive the relationship between current, voltage, and resistance in Ohm’s Law.
4. How does temperature affect the resistance of a conductor?
5. How would the equivalent resistance change if $R_2$ in question 1 was $6\ \Omega$ instead of $12\ \Omega$?

Tip: When solving resistor networks, always identify whether the resistors are in series or parallel to simplify the circuit efficiently.