The equivalent resistance is calculated as follows:
\[ R_{\text{eq}} = \frac{15 \times 10}{15 + 10} = \frac{150}{25} = 6 \, \Omega \]
Diode 2 is in reverse bias, so no current will flow through the branch containing it. It can be treated as a broken wire.
Diode 1 is in forward bias and will behave as a conducting wire. The new circuit becomes a simpler parallel and series resistor network.
A battery of emf \( E \) and internal resistance \( r \) is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of \( E \) and \( r \).
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is: