A single phase voltage controller has input of 230 V and a load of 15 Ω resistive. For 6 cycles on and 4 cycles off, determine the rms output voltage.

To determine the RMS output voltage of a single-phase voltage controller with the given parameters, we can use the formula for the RMS output voltage from a phase control circuit.

1. The input voltage (V_in) is 230 V.
2. The load resistance (R) is 15 Ω.
3. The duty cycle is defined based on the on and off cycles: the controller is on for 6 cycles and off for 4 cycles.

The total number of cycles is 6 (on) + 4 (off) = 10 cycles. The duty cycle (D) is therefore:

[ D = frac{text{on time}}{text{total time}} = frac{6}{10} = 0.6 ]

Next, we calculate the RMS output voltage (V_out) using the formula:

[ V_{out} = V_{in} times D = V_{in} times frac{text{on time}}{text{total time}} ]

Substituting the known values:

[ V_{out} = 230 , V times 0.6 = 138 , V ]

Therefore, the RMS output voltage of the controller is 138 V.