An ac source is connected to a resistive circuits. Which of the following statements are false ?

Options

A. Current lead ahead of voltage in phase
B. Current lags behind voltage in phase
C. Current and voltage are in same phase
D. Any of the above may be true depending upon the value of resistance

Answer

To solve the question about the AC source connected to a resistive circuit and identify the false statements, we can follow these steps:

### Step 1: Understand the AC Circuit
An AC source provides a voltage that varies sinusoidally with time. In a resistive circuit, the voltage and current are related by Ohm's law, which states that \( V = IR \), where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance.

### Step 2: Analyze the Phase Relationship
In a purely resistive circuit, the current and voltage are in phase. This means that the phase difference (\( \phi \)) between the voltage and current is zero:
\[ \phi = 0 \]

### Step 3: Write the Voltage and Current Equations
The voltage supplied by the AC source can be expressed as:
\[ V(t) = V_0 \sin(\omega t) \]
The current flowing through the circuit can be expressed as:
\[ I(t) = I_0 \sin(\omega t + \phi) \]
Since \( \phi = 0 \) in a resistive circuit, we have:
\[ I(t) = I_0 \sin(\omega t) \]

### Step 4: Evaluate the Statements
Now we need to evaluate the given statements regarding the relationship between voltage and current in a resistive circuit:

1. **Current leads ahead of the voltage**: This is false. In a resistive circuit, current and voltage are in phase, meaning they reach their maximum and zero values simultaneously.

2. **Current lags behind the voltage**: This is also false. Again, in a resistive circuit, current and voltage are in phase.

3. **Current and voltage are in the same phase**: This is true. In a purely resistive circuit, the current and voltage waveforms coincide.

4. **Any of the values may be true depending upon the value of the resistance**: This is false. The relationship between current and voltage in a purely resistive circuit is always the same; they are always in phase regardless of the resistance value.

### Step 5: Identify the False Statements
From the analysis, we can conclude that the false statements are:
- Current leads ahead of the voltage.
- Current lags behind the voltage.
- Any of the values may be true depending upon the value of the resistance.

### Final Answer
The false statements are:
1. Current leads ahead of the voltage.
2. Current lags behind the voltage.
3. Any of the values may be true depending upon the value of the resistance.