First, we calculate the equivalent resistance \( R_{eq} \) of the circuit.
The two branches with \( 2 \, \Omega \) resistors are in parallel. The equivalent resistance for each pair of resistors in parallel is:
\[ \frac{1}{R_{eq}} = \frac{1}{2} + \frac{1}{2} = 1 \, \Omega. \]Since there are two such parallel branches in series, the total resistance \( R_{eq} \) of the circuit is:
\[ R_{eq} = 1 + 1 + \frac{2}{3} = \frac{4}{3} \, \Omega. \]The power \( P \) consumed in the circuit is given by:
\[ P = \frac{V^2}{R_{eq}}. \]Substitute \( V = 2 \, V \) and \( R_{eq} = \frac{4}{3} \, \Omega \):
\[ P = \frac{2^2}{\frac{4}{3}} = \frac{4}{\frac{4}{3}} = 3 \, W. \]Thus, the power consumption in the entire circuit is:
\[ 3 \, W. \]Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32