If V=100sin (100t)V and I =100sin `(100t+(pi)/(3))` mA are the instantaneous values of voltage and current, respectively

Options

A. `70.7 V, 70.7 mA`
B. `70.7 V, 70.7 A`
C. `141.4 V,141.4 mA`
D. `100 V,100 mA`

Explanation

To solve the problem, we need to find the root mean square (RMS) values of the given voltage and current equations. Let's break down the steps:

### Step 1: Identify the Voltage Equation
The voltage equation is given as:
\[ V = 100 \sin(100t) \, \text{V} \]

### Step 2: Compare with General Voltage Equation
The general form of the voltage equation is:
\[ V = V_0 \sin(\omega t) \]
By comparing, we can identify:
- \( V_0 = 100 \, \text{V} \)
- \( \omega = 100 \, \text{rad/s} \)

### Step 3: Calculate RMS Voltage
The RMS voltage (\( V_{\text{rms}} \)) is calculated using the formula:
\[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \]
Substituting the value of \( V_0 \):
\[ V_{\text{rms}} = \frac{100}{\sqrt{2}} \approx 70.7 \, \text{V} \]

### Step 4: Identify the Current Equation
The current equation is given as:
\[ I = 100 \sin\left(100t + \frac{\pi}{3}\right) \, \text{mA} \]

### Step 5: Compare with General Current Equation
The general form of the current equation is:
\[ I = I_0 \sin(\omega t + \phi) \]
By comparing, we can identify:
- \( I_0 = 100 \, \text{mA} \)
- \( \omega = 100 \, \text{rad/s} \)
- \( \phi = \frac{\pi}{3} \)

### Step 6: Calculate RMS Current
The RMS current (\( I_{\text{rms}} \)) is calculated using the formula:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
Substituting the value of \( I_0 \):
\[ I_{\text{rms}} = \frac{100}{\sqrt{2}} \approx 70.7 \, \text{mA} \]

### Final Results
- The RMS voltage is \( 70.7 \, \text{V} \)
- The RMS current is \( 70.7 \, \text{mA} \)

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