12. The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in a time $\Delta t$. Then the total quantity of electric charge $Q$ that passes any point in the circuit during the time $\Delta t$ is represented by: (2004)

$Q = \frac{\Delta \phi}{R}$

$Q = \frac{\Delta \phi}{\Delta t}$

$Q = R \cdot \frac{\Delta \phi}{\Delta t}$

$Q = \frac{1}{2} \frac{\Delta \phi}{\Delta t}$

Solution:

The induced emf is $e = \frac{\Delta \phi}{\Delta t}$.
The induced current is $I = \frac{e}{R} = \frac{\Delta \phi}{R \Delta t}$.
Total charge $Q = I \Delta t = \frac{\Delta \phi}{R \Delta t} \cdot \Delta t = \frac{\Delta \phi}{R}$.

Rankers Physics

12. The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in a time $\Delta t$. Then the total quantity of electric charge $Q$ that passes any point in the circuit during the time $\Delta t$ is represented by: (2004)

Solution:

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