Pure resistor, current and voltage are in same phase in which graph?

Options

A.
B.
C.
D.

Explanation

To determine in which graph the current and voltage are in the same phase for a pure resistor, we can analyze the relationship between voltage and current in an AC circuit.

### Step-by-Step Solution:

1. **Understanding the AC Voltage and Current Equations**:
- For a pure resistor, the voltage (V) across it can be expressed as:
\[ V = V_m \sin(\omega t) \]
- The current (I) through the resistor can also be expressed similarly:
\[ I = I_m \sin(\omega t) \]

2. **Identifying the Phase Relationship**:
- In the case of a pure resistor, both the voltage and current equations have the same sine function with the same angular frequency (\(\omega\)). This indicates that they reach their maximum values at the same time.

3. **Calculating the Phase Difference**:
- The phase difference (\(\Delta \phi\)) between voltage and current can be calculated as:
\[ \Delta \phi = \phi_V - \phi_I \]
- Since both voltage and current are represented by the same sine function, we have:
\[ \Delta \phi = 0 \]

4. **Conclusion**:
- A phase difference of 0 means that the current and voltage are in phase. Therefore, in a graph depicting voltage and current over time, the peaks and zero crossings of both waveforms will align perfectly.

5. **Identifying the Correct Graph**:
- The graph that shows the voltage and current waveforms with their peaks and troughs aligned (i.e., both reach their maximum and minimum values simultaneously) is the correct representation of a pure resistor.

### Final Answer:
The graph where the current and voltage are in the same phase is the one showing both waveforms aligned with a phase difference of 0.

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