A power outlet puts out 60 Hz AC. Which of the following statements is true ?

Options

A. Voltage goes to zero only 120 times per second
B. Current goes to zero only 60 times per second
C. Power goes to zero, only 60 times per second
D. Voltage , current and power stay constant

Answer

To determine which statement is true regarding a power outlet that puts out 60 Hz AC, we will analyze each statement step by step.

### Step 1: Understanding the Frequency
The frequency of the AC is given as 60 Hz. This means that the alternating current completes 60 cycles in one second.

**Hint:** Remember that frequency (in Hz) indicates how many cycles occur in one second.

### Step 2: Analyzing Voltage
In an AC circuit, the voltage varies sinusoidally. The voltage can be expressed as:
\[ V(t) = V_0 \sin(\omega t) \]
where \( \omega = 2\pi f \) and \( f \) is the frequency.

Since the frequency is 60 Hz, the voltage will go to zero at two points in each cycle (one positive peak and one negative peak). Therefore, in one second (60 cycles), the voltage goes to zero:
\[ 60 \text{ cycles} \times 2 = 120 \text{ times} \]

**Hint:** For every complete cycle of AC, the voltage crosses zero twice.

### Step 3: Analyzing Current
The current in an AC circuit is also sinusoidal and can be expressed similarly:
\[ I(t) = I_0 \sin(\omega t) \]
The current will also go to zero at the same points as the voltage, which means it goes to zero 120 times per second, not just 60.

**Hint:** The current behaves similarly to the voltage in an AC circuit; both go to zero at the same points in their cycles.

### Step 4: Analyzing Power
The instantaneous power in an AC circuit is given by:
\[ P(t) = I^2 R \]
Substituting the expression for current:
\[ P(t) = (I_0 \sin(\omega t))^2 R = I_0^2 R \sin^2(\omega t) \]
The sine squared function goes to zero at the same points as the sine function, meaning the power also goes to zero 120 times per second.

**Hint:** Power in an AC circuit is related to the square of the current, which means it will also have the same zero crossings as the current.

### Step 5: Evaluating the Statements
- **Statement A:** Voltage goes to 0 only 120 times per second. **True**
- **Statement B:** Current goes to 0 only 60 times per second. **False**
- **Statement C:** Power goes to 0 only 60 times per second. **False**
- **Statement D:** Voltage, current, and power stay constant. **False**

### Conclusion
The only true statement is that the voltage goes to zero 120 times per second.

**Final Answer:** The true statement is: **Voltage goes to 0 only 120 times per second.**