Question 5: Current Electricity

Question

The reading of the ammeter $(A)$ in steady state for the given circuit (assuming negligible internal resistance of the ammeter) is ______ $	ext{A}$.

Accepted Answer

$\$In a DC circuit, after a long time, the capacitor behaves like an open circuit (infinite resistance). $\$Therefore, no current flows through the branch containing the $10,\mu	ext{F}$ capacitor and the $8\Omega$ resistor in series with it.$\$

The two resistors $R_4$ and $R_5$ (each $8\Omega$) are in parallel:$\$

$R_{4,5} = \frac{8 	imes 8}{8 + 8} = \frac{64}{16} = 4\Omega$ $\$

This equivalent resistance is in series with $R_3 = 4\Omega$: $\$

$R_{3,4,5} = 4 + 4 = 8\Omega$ $\$

Now this combination is in parallel with $R_2 = 8\Omega$: $\$

$R_{2,3,4,5} = \frac{8 	imes 8}{8 + 8} = 4\Omega$ $\$

Finally, this is in series with $R_1 = 1\Omega$: $\$

$R_{	ext{total}} = 1 + 4 = 5\Omega$

Current Calculation

Using Ohm’s Law:

$i = \frac{V}{R_{	ext{total}}} = \frac{10}{5} = 2,	ext{A}$

So, total current $i = i_1 = 2,	ext{A}$

Current Distribution

Since $R_2$ and $R_{3,4,5}$ are equal ($8\Omega$ each before reduction), current splits equally:

$i_2 = i_3$

Using Kirchhoff’s Current Law:

$i = i_2 + i_3 = 2i_3 \Rightarrow i_3 = \frac{i}{2} = \frac{2}{2} = 1,	ext{A}$

Final Answer

The ammeter reads:

$\boxed{1,	ext{A}}$

Answer

$\frac{1}{2}$

Answer

$1$

Answer

$2$

Answer

$0$

Current Electricity

The reading of the ammeter (A) in steady state for the given circuit (assuming negligible internal resistance of the ammeter) is ______ \text{A}.

Choose the correct answer: