To solve the problem step by step, we will analyze the two devices, P and Q, and then find the current when they are connected in series.
### Step 1: Analyze Device P
- Given:
- Voltage (V) = 220 V
- Current (I) = 0.25 A
- Phase angle (φ) = π/2 radians (current leads voltage)
Since the current leads the voltage by π/2, device P behaves like a capacitor. The reactance (Xc) can be calculated using:
\[
X_c = \frac{V}{I} = \frac{220 \, \text{V}}{0.25 \, \text{A}} = 880 \, \Omega
\]
### Step 2: Analyze Device Q
- Given:
- The same voltage (V) = 220 V
- The same current (I) = 0.25 A
- Phase angle (φ) = 0 radians (current is in phase with voltage)
Since the current is in phase with the voltage, device Q behaves like a resistor. The resistance (R) can be calculated using:
\[
R = \frac{V}{I} = \frac{220 \, \text{V}}{0.25 \, \text{A}} = 880 \, \Omega
\]
### Step 3: Combine Devices P and Q in Series
When devices P and Q are connected in series, the total impedance (Z) of the circuit can be calculated using the formula:
\[
Z = \sqrt{R^2 + X_c^2}
\]
Substituting the values we found:
\[
Z = \sqrt{(880 \, \Omega)^2 + (880 \, \Omega)^2} = \sqrt{2 \times (880 \, \Omega)^2} = 880\sqrt{2} \, \Omega
\]
### Step 4: Calculate the Total Current in the Series Circuit
Using Ohm's law, the total current (I_total) in the series circuit can be calculated as:
\[
I_{\text{total}} = \frac{V}{Z} = \frac{220 \, \text{V}}{880\sqrt{2} \, \Omega}
\]
Simplifying this:
\[
I_{\text{total}} = \frac{220}{880\sqrt{2}} = \frac{1}{4\sqrt{2}} \, \text{A}
\]
### Step 5: Determine the Phase Angle
To find the phase angle (φ) of the total current with respect to the voltage, we can use:
\[
\tan \phi = \frac{X_c}{R} = \frac{880 \, \Omega}{880 \, \Omega} = 1
\]
Thus, φ = 45 degrees (or π/4 radians), indicating that the current leads the voltage.
### Final Answer
The current when the same source is connected across a series combination of devices P and Q is:
\[
I_{\text{total}} = \frac{1}{4\sqrt{2}} \, \text{A} \quad \text{(leading the voltage by } \frac{\pi}{4} \text{ radians)}
\]
