If we increase the driving frequency in a circuit with a purely resistive load, do (a) amplitude `V_R` and (b) amplitude `I_R` increase , decrease, or remain the same ?

Answer

To solve the question regarding the effect of increasing the driving frequency in a circuit with a purely resistive load on the amplitudes \( V_R \) and \( I_R \), we can follow these steps:

### Step 1: Understand the Circuit
In a purely resistive circuit, the load consists only of a resistor (R) connected to an AC voltage source. The relationship between voltage (V), current (I), and resistance (R) is given by Ohm's Law:
\[ V = I \cdot R \]

### Step 2: Analyze the Effect of Frequency on a Resistive Load
For a purely resistive load, the impedance (Z) is equal to the resistance (R). The impedance does not depend on frequency. Therefore, when the frequency of the AC source is increased, the impedance remains constant.

### Step 3: Determine the Amplitude of Voltage \( V_R \)
The amplitude of the voltage across the resistor \( V_R \) is determined by the voltage source. Since the impedance does not change with frequency, and there are no reactive components (like inductors or capacitors) that would affect the voltage, the amplitude \( V_R \) remains constant regardless of the frequency change.

### Step 4: Determine the Amplitude of Current \( I_R \)
Using Ohm's Law, we can express the current amplitude \( I_R \) as:
\[ I_R = \frac{V_R}{R} \]
Since \( V_R \) remains constant (as established in Step 3) and \( R \) is also constant, the amplitude of the current \( I_R \) will also remain constant.

### Conclusion
(a) The amplitude \( V_R \) remains the same.
(b) The amplitude \( I_R \) remains the same.

### Summary of Results
- \( V_R \): Remains the same
- \( I_R \): Remains the same