Find the heat produced in the external circuit \( (AB) \) in one second.
Show Hint
For circuit problems:
\begin{itemize}
\item Reduce complex resistor networks stepwise
\item Use \( P = I^2R \) for heat or power calculation
\item Heat produced \( H = Pt \)
\end{itemize}
Step 1: Reduce the network between points \( A \) and \( B \).
The upper and lower arms form a Wheatstone-bridge–like network with a central \(1\,\Omega\) resistor.
On simplifying the internal network, the equivalent resistance between \( A \) and \( B \) is:
\[
R_{AB} = 2\,\Omega
\]
Step 2: The external circuit includes an additional \(1\,\Omega\) resistor in series with the battery.
\[
R_{\text{total}} = R_{AB} + 1 = 3\,\Omega
\]
Step 3: Current in the circuit:
\[
I = \frac{V}{R_{\text{total}}} = \frac{9}{3} = 3\,\text{A}
\]
Step 4: Power dissipated in the external circuit \( AB \):
\[
P_{AB} = I^2 R_{AB} = 3^2 \times 2 = 18\,\text{W}
\]
Step 5: Heat produced in one second:
\[
H = P_{AB} \times t = 18 \times 1 = 1207.50\,\text{J}
\]
