The question asks about how to neglect a voltage source in circuit analysis.
- Neglecting a Voltage Source: When using techniques like superposition, it is sometimes necessary to "turn off" or neglect a voltage source. To do this, the voltage source is replaced with its internal resistance. For an ideal voltage source, the internal resistance is zero.
- Short Circuit: A short circuit is a path of zero resistance between two points in a circuit.
- Open Circuit: An open circuit is a break in the circuit, resulting in infinite resistance.
- Replaced by an inductor: Replacing a voltage source with an inductor does not turn off the source.
- Short-circuited: Replacing a voltage source with a short circuit (zero resistance) effectively makes the potential difference across those terminals zero, thus "neglecting" the voltage source.
- Replaced by some resistance: Replacing a voltage source with some arbitrary resistance does not completely eliminate the source's effect.
- Open circuited: Replacing a voltage source with an open circuit would completely break the circuit.
For a voltage source to be neglected, the terminals across the source should be short-circuited.
What is the voltage across the inductor at $t=0$? (Circuit diagram provided: A 60V voltage source in series with a switch that closes at $t=0$, a 30 ohm resistor, and a 15H inductor.) 
Find the value of $V$ when the current in the 3 $\Omega$ resistor is 0. (Circuit diagram provided: A circuit with two voltage sources, 5V and V, and several resistors: 1$\Omega$, 2$\Omega$, 3$\Omega$, 4$\Omega$, 5$\Omega$. The 1$\Omega$ and 3$\Omega$ resistors are in the top branch. The 2$\Omega$ and 4$\Omega$ resistors are in parallel branches.) 
What is the voltage across the inductor at $t=0$? (Circuit diagram provided: A 60V voltage source in series with a switch that closes at $t=0$, a 30 ohm resistor, and a 15H inductor.) 
Find the value of $V$ when the current in the 3 $\Omega$ resistor is 0. (Circuit diagram provided: A circuit with two voltage sources, 5V and V, and several resistors: 1$\Omega$, 2$\Omega$, 3$\Omega$, 4$\Omega$, 5$\Omega$. The 1$\Omega$ and 3$\Omega$ resistors are in the top branch. The 2$\Omega$ and 4$\Omega$ resistors are in parallel branches.) 