
- **Option A:** In a purely capacitive circuit, the voltage (V) lags the current (I) by 90°. Therefore, **A-I** is correct.
- **Option B:** In a purely inductive circuit, the voltage (V) leads the current (I) by 90°. Therefore, **B-II** is correct.
- **Option C:** In an LCR series circuit at resonance, the inductive reactance (XL) equals the capacitive reactance (XC), resulting in a purely resistive behavior where the voltage and current are in phase. Therefore, **C-III** is correct.
- **Option D:** In a general LCR series circuit, the voltage and current are out of phase by an angle θ, which depends on the relative values of XL and XC. Therefore, **D-IV** is correct.
**Answer:** A-I, B-II, C-III, D-IV (Option 4)
A laser beam has intensity of $4.0\times10^{14}\ \text{W/m}^2$. The amplitude of magnetic field associated with the beam is ______ T. (Take $\varepsilon_0=8.85\times10^{-12}\ \text{C}^2/\text{N m}^2$ and $c=3\times10^8\ \text{m/s}$)
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.