The Question is from NEET guide , and it was created by the author NAGA SAI

Question

Consider a capacitor - charging circuit. Let $Q_1$ be the charge given to the capacitor in time interval of $20 \mathrm{~ms}$ and $Q_2$ be the charge given in the next time interval of $20 \mathrm{~ms}$. Let $10 \mu \mathrm{Ccharge}$ be deposited in a time interval $t_1$ and the next $10 \mu \mathrm{C~charge}$ is deposited in the next time interval $t_2$. Then,

NAGA SAI · Accepted Answer

## CORE INFORMATION ✓ **Answer**: B ## CONCEPT FRAMEWORK **Primary Concept**: The charging behavior of capacitors in RC circuits. **Related Topics**: Exponential growth of charge, time constant of RC circuit, capacitor behavior over time. **Prerequisites**: Basic understanding of capacitors, charging equations, and the concept of time constant in RC circuits. ## SOLUTION PATHWAY **Given Information**: 1. Capacitor charge amounts: $Q_1$ and $Q_2$. 2. Time intervals: $t_1$ and $t_2$ each equal to $20 \mathrm{ms}$. **Method & Steps**: 1. Analyze the charging process of a capacitor. Reasoning: A capacitor charges according to the equation $Q(t) = Q_{max}(1 - e^{-t/RC})$ where $Q_{max}$ is the maximum charge, $R$ is resistance, and $C$ is capacitance. Formula/Rule: The charging curve is exponential. 2. Determine the relationship between $Q_1$ and $Q_2$. Working: In the first interval $t_1$, the capacitor has not yet reached its maximum charge, so $Q_1$ will be larger due to the ongoing charging process. In the next interval $t_2$, the charge increases at a slower rate since the capacitor is closer to being fully charged. Key Point: The rate of charging decreases as the capacitor approaches maximum charge. 3. Compare the time intervals $t_1$ and $t_2$. Result: Since $t_2$ is after $t_1$, $t_2$ will take longer to reach the same amount of charge, thus $t_1 < t_2$. Verification: The exponential nature of charging confirms that $Q_1 > Q_2$ and $t_1 < t_2$. ## OPTION ANALYSIS [A] :x: This option suggests $Q_1 > Q_2$, but states $t_1 > t_2$, which contradicts the charging behavior. [B] ✓: Correct, as $Q_1$ is greater than $Q_2$ and $t_1$ is less than $t_2$. [C] :x: Incorrect as it states $Q_1 < Q_2$, which is not true based on the charging nature. [D] :x: This option is incorrect since it suggests $Q_1 < Q_2$. ## LEARNING AIDS **Common Mistakes**: 1. Misunderstanding exponential charging: Remember that the charging rate decreases over time. 2. Confusing time intervals: Ensure to analyze the order of intervals in relation to charging behavior. **Quick Tips**: 1. Use the charging formula to visualize charge accumulation over time. 2. Keep in mind that the closer a capacitor is to being fully charged, the slower the rate of charge increase.

NAGA SAI · Answer

$Q_1 > Q_2, t_1 > t_2$

NAGA SAI · Answer

The correct Option is "$Q_1 > Q_2, t_1 < t_2$"

NAGA SAI · Answer

$Q_1 < Q_2, t_1 > t_2$

NAGA SAI · Answer

$Q_1 < Q_2, t_1 < t_2$

NEET Questions

Select Subject

Question Tags

NEET Subjects

Our Bots

Company