To determine the input power factor (pf) for the single phase voltage controller, we can start with the given values:

1. Input Voltage (V) = 230 V
2. Load Resistance (R) = 15 Ω
3. On and Off Cycles: 6 cycles on and 4 cycles off.

### Step 1: Calculate the Average Voltage (V_avg)

The total cycle duration can be calculated based on the number of cycles on and off. Each cycle can be assumed to be 1 unit of time; hence for 10 cycles (6 on + 4 off):

– Time on = 6

– Time off = 4

– Total time = 10 cycles

The average voltage can be calculated as

[

V_{avg} = V cdot frac{T_{on}}{T_{total}} = 230 cdot frac{6}{10} = 138 V

]

### Step 2: Calculate the Load Current (I)

Using Ohm’s Law ( I = frac{V_{avg}}{R} ):

[

I = frac{V_{avg}}{R} = frac{138 V}{15 Ω} = 9.2 A

]

### Step 3: Calculate Active Power (P)

The active power consumed by the resistive load can be calculated using the formula:

[

P = I^2