iran-konkur 2024 Q67

iran-konkur · Other · konkur-riazi_1403_ordibehesht_specialized Not Maths
67. The magnetic flux passing through a coil varies according to the graph below. If the magnitude of the induced EMF in the coil during the time intervals (zero to $t_1$), ($t_1$ to $t_2$), and ($t_2$ to $t_3$) are $\varepsilon_1$, $\varepsilon_2$, and $\varepsilon_3$ respectively, which relation is correct?
[Figure: Graph of $\varphi$ vs $t$, showing flux rising to $\varphi_{\max}$ at $t_1$, then decreasing linearly to $-\varphi_{\max}$ at $t_2 = 2t_1$, then increasing linearly back to zero at $t_3 = 3t_1$]
  • [(1)] $\varepsilon_1 = 2\varepsilon_3$ and $\varepsilon_2 = 0$
  • [(2)] $\varepsilon_1 = 2\varepsilon_2 = 2\varepsilon_3$
  • [(3)] $\varepsilon_3 = 2\varepsilon_1$ and $\varepsilon_2 = 0$
  • [(4)] $\varepsilon_1 = 2\varepsilon_3 = \varepsilon_2$

\textbf{67.} The magnetic flux passing through a coil varies according to the graph below. If the magnitude of the induced EMF in the coil during the time intervals (zero to $t_1$), ($t_1$ to $t_2$), and ($t_2$ to $t_3$) are $\varepsilon_1$, $\varepsilon_2$, and $\varepsilon_3$ respectively, which relation is correct?

\textit{[Figure: Graph of $\varphi$ vs $t$, showing flux rising to $\varphi_{\max}$ at $t_1$, then decreasing linearly to $-\varphi_{\max}$ at $t_2 = 2t_1$, then increasing linearly back to zero at $t_3 = 3t_1$]}

\begin{itemize}
    \item[(1)] $\varepsilon_1 = 2\varepsilon_3$ and $\varepsilon_2 = 0$
    \item[(2)] $\varepsilon_1 = 2\varepsilon_2 = 2\varepsilon_3$
    \item[(3)] $\varepsilon_3 = 2\varepsilon_1$ and $\varepsilon_2 = 0$
    \item[(4)] $\varepsilon_1 = 2\varepsilon_3 = \varepsilon_2$
\end{itemize}

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