An ac voltmeter with large impedance is connected in turn across the inductor, the capacitor, and the resistor in a series circuit having an alternating emf of 125 V (rms), the meter gives the same reading in volts in each case. What is this reading?

Answer

To solve the problem, we need to analyze the behavior of the AC voltmeter when connected across the inductor, capacitor, and resistor in a series RLC circuit with an alternating emf of 125 V (rms).

### Step-by-Step Solution:

1. **Understanding the Circuit**:
- We have a series RLC circuit with an alternating emf (E) of 125 V (rms).
- The voltmeter gives the same reading across the inductor (VL), capacitor (VC), and resistor (VR).

2. **RMS Voltage**:
- The given emf is 125 V (rms), which means the total voltage across the circuit is 125 V when measured in rms.

3. **Voltage Across Components**:
- In an RLC series circuit, the voltages across the inductor, capacitor, and resistor can be expressed as:
- \( V_R = I \cdot R \)
- \( V_L = I \cdot X_L \) (where \( X_L = \omega L \))
- \( V_C = I \cdot X_C \) (where \( X_C = \frac{1}{\omega C} \))
- Here, \( I \) is the current through the circuit.

4. **Impedance in the Circuit**:
- The total impedance \( Z \) of the circuit is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
- Since the voltmeter reads the same voltage across each component, we can say:
\[ V_R = V_L = V_C \]

5. **Using the Voltage Relationship**:
- Since the voltmeter reads the same voltage across each component, we can denote this common reading as \( V \).
- Therefore, we have:
\[ V_R = V_L = V_C = V \]

6. **Applying Kirchhoff's Voltage Law**:
- According to Kirchhoff's law, the total voltage in the circuit is the sum of the voltages across each component:
\[ V_R + V_L + V_C = E \]
- Substituting the common voltage \( V \):
\[ V + V + V = 125 \, \text{V} \]
- This simplifies to:
\[ 3V = 125 \, \text{V} \]

7. **Calculating the Voltage Reading**:
- Solving for \( V \):
\[ V = \frac{125 \, \text{V}}{3} \approx 41.67 \, \text{V} \]

### Final Answer:
The reading on the AC voltmeter when connected across the inductor, capacitor, and resistor is approximately **41.67 V**.