Same current is flowing in two alternating circuits. The first circuit contains only inductances and the other contains only a capacitor, if the frequency of the e.m.f of AC is increased, the effect on the value of the current will be

Options

A. increased in the first circuit an decreased in the other
B. increased in both circuits
C. decreased in both the circuits
D. decreased in the first circuit and increased in the other

Answer

To solve the problem, we need to analyze the behavior of current in two alternating circuits: one with only inductance and the other with only capacitance, when the frequency of the alternating current (AC) is increased.

### Step-by-Step Solution:

1. **Understanding the Circuits**:
- Circuit 1: Contains only an inductor (L).
- Circuit 2: Contains only a capacitor (C).
- Both circuits have the same current flowing through them.

2. **Inductive Circuit Analysis**:
- The inductive reactance \(X_L\) is given by the formula:
\[ X_L = \omega L \]
where \(\omega = 2\pi f\) (angular frequency) and \(f\) is the frequency of the AC.
- The relationship between voltage (V), current (I), and inductive reactance is:
\[ V = I_L \cdot X_L \implies I_L = \frac{V}{X_L} = \frac{V}{\omega L} \]
- As the frequency \(f\) increases, \(\omega\) increases, which causes \(X_L\) to increase. Therefore, \(I_L\) (the current through the inductor) decreases.

3. **Capacitive Circuit Analysis**:
- The capacitive reactance \(X_C\) is given by:
\[ X_C = \frac{1}{\omega C} \]
- The relationship for the capacitive circuit is:
\[ V = I_C \cdot X_C \implies I_C = \frac{V}{X_C} = V \cdot \omega C \]
- As the frequency \(f\) increases, \(\omega\) increases, which causes \(X_C\) to decrease. Therefore, \(I_C\) (the current through the capacitor) increases.

4. **Conclusion**:
- In summary, as the frequency of the AC increases:
- The current through the inductor \(I_L\) decreases.
- The current through the capacitor \(I_C\) increases.
- Thus, the effect of increasing the frequency on the value of the current is that the current in the inductive circuit decreases while the current in the capacitive circuit increases.

### Final Answer:
- The current in the inductive circuit decreases, while the current in the capacitive circuit increases.