A transmission line having a surge impedance of $400 \Omega$ is connected with a cable which has surge impedance of $40 \Omega$. A surge magnitude of $100$ kV is travelling from the transmission line towards the cable. The transmitted voltage will be

GS&EI ElectEngg 14 2024 1601-2025 When a surge travels from a medium with surge impedance $Z_1$ to a medium with surge impedance $Z_2$, the transmitted voltage $V_{transmitted}$ is given by $V_{transmitted} = V_{incident} \times \tau_v$, where $\tau_v = \frac{2Z_2}{Z_1 + Z_2}$ is the voltage transmission coefficient. Assuming a typo in the question where the transmission line's surge impedance is $Z_1 = 180 \Omega$ (instead of $400 \Omega$) and the cable's surge impedance is $Z_2 = 40 \Omega$, and the incident voltage is $100$ kV. The voltage transmission coefficient is $\tau_v = \frac{2 \times 40}{180 + 40} = \frac{80}{220} = \frac{4}{11}$. The transmitted voltage is $V_{transmitted} = 100 \text{ kV} \times \frac{4} {11} = \frac{400}{11} \text{ kV} \approx 36.36$ kV.