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Get Answers to all your Questions
A uniform thin rod AB of length L has linear mass density , where x is measured from A. If the CM of the rod lies at a distance of
from A, then a and b are related as :
Answers (1)
To solve this question, we need to find the **charge on capacitor $C_1$ in steady state**.
---
###**Given:**
* $R_1 = 10\,\Omega$
* $C_1 = 1\,\mu\text{F}$
* $C_2 = 2\,\mu\text{F}$
* $E = 6\,\text{V}$ (Battery)
---
###**Concept Used:**
In **steady state**, capacitors act as **open circuits** because current stops flowing through them. So, **no current flows through the resistor** either. The potential across each capacitor is determined by **charge distribution and voltage division**.
Now let's look at a likely configuration:
* $C_1$ and $C_2$ are in **series** (from the nature of such standard problems).
* Battery $E = 6\,\text{V}$ is connected across the series combination of $C_1$ and $C_2$
---
### **Step 1: Equivalent Capacitance in Series**
$$
\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} = \frac{1}{1} + \frac{1}{2} = \frac{3}{2}
\Rightarrow C_{\text{eq}} = \frac{2}{3}\,\mu\text{F}
$$
---
### **Step 2: Total Charge in Series Capacitors**
In series, **charge on each capacitor is same**.
$$
Q = C_{\text{eq}} \cdot V = \frac{2}{3} \cdot 6 = 4\,\mu\text{C}
$$
So,
$$
Q_1 = Q_2 = \boxed{4\,\mu\text{C}}
$$
---
###**Final Answer:**
$$
\boxed{4\,\mu\text{C}}
$$
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