An LCR circuit with R=70 ohms in series with a parallel combination of L=1.5H and C=30micro faraday's is driven by a 230v supply with angular frequency of 300 rad/s (I) find the power input current ?

To find the power input current, we first need to calculate the impedance of the LCR circuit.

The impedance of the resistor (R) is simply R = 70 ohms.

The impedance of the inductor (L) is given by XL = ωL = 300 * 1.5 = 450 ohms.

The impedance of the capacitor (C) is given by XC = 1 / (ωC) = 1 / (300 * 30 * 10^-6) = 1 / 9 = 0.111 ohms.

Now, the total impedance of the parallel combination of L and C is given by ZLC = 1 / (1/XL + 1/XC) = 1 / (1/450 + 1/0.111) = 0.109 ohms.

The total impedance of the LCR circuit is then given by Z = sqrt(R^2 + ZLC^2) = sqrt(70^2 + 0.109^2) = 70.001 ohms.

The power input current can be calculated using Ohm's Law: I = V / Z = 230 / 70.001 = 3.285 A.

Therefore, the power input current is 3.285 A.

Step 1: Calculate the impedance of the parallel combination

```
Xc = 1 / (2πfC) = 1 / (2π - 300 - 30 - 10^-6) = 111.11 ohms

Zl = sqrt(L^2 + XL^2) = sqrt(1.5^2 + 111.11^2) = 111.84 ohms

Zp = Zl - Xc / (Zl + Xc) = 111.11 - 111.84 / (111.84 + 111.11) = 56.7 ohms
```

Step 2: Calculate the total impedance of the circuit

```
Z = R + Zp = 70 + 56.7 = 126.7 ohms
```

Step 3: Calculate the current

```
I = V / Z = 230 / 126.7 = 1.82 amps
```

Therefore, the power input current is 1.82 amps.