Imagine that you have three circuit elements: a single bulb, a piece of wire, and a battery. You start by keeping these three elements separate and unconnected. You use a voltmeter to measure the voltage across each of the three elements. Then, you connect the bulb, wire, and battery together to form a complete circuit, so that the bulb lights up. You repeat the measurements you made before, using the voltmeter to measure the voltage across each element while it is in the complete circuit. For the questions below, assume that the battery and the wire are ideal.

a. Compare the voltage across the battery: a) when the battery is by itself vs b) when the battery is part of the complete circuit. Is the voltage across the battery different in these two situations, or is the voltage the same? Explain your answer.
b. Compare the voltage across the bulb: a) when the bulb is by itself vs b) when the bulb is part of the complete circuit. Is the voltage across the bulb different in these two situations, or is it the same? Explain.
c. Now compare the voltage across the piece of wire: a) when the wire is by itself vs b) when the wire is part of the complete circuit. Is the voltage across the piece of wire different in these two situations, or is it the same? Explain your answer.
d. Now consider only the situation in which the battery, wire, and bulb have been arranged to form a complete circuit in which the bulb lights up. For this situation, rank i) the voltage across the battery, ii) the voltage across the bulb, and iii) the voltage across the piece of wire, according to their absolute values, from greatest to smallest. If any are the same, or if any are zero, state that explicitly. Explain your reasoning.

b) the battery is connected to the lamp this takes something current, but the electromotive force does not change therefore the voltage is Vo; This is because the battery's energy comes from a chemical reaction of the elements inside it.

in summary the two voltages are equal

B) voltage Lamp

a) when the bulb is single, its voltage is zero V = 0

since it has no energy

b) when in the circuit V = V₀ - V_r

where V_r is the voltage across the wire, due to its resistance, the energy for these voltages is given by the battery

in this case the two voltages are different

C) the voltage across the wire

a) unconnected V = 0

b) connected V = V₀ - V_L

where V_L is the voltage across the lamp due to its resistance

we can write the wire voltage

V_r = i R

as they indicate that the wire is ideal, its resistance is zero R = 0, consequently

V_r = 0

the voltage is the same V = 0

D) circuit voltage

For this part we must write Ohm's law for this circuit

V₀ = V_L + V_r

where V₀ is the battery voltage, V_L and V_r are the voltage of the lamp and the wire, respectively.

The voltage of each element is

V_L = i R_L

V_r = i R

This is a series circuit so the current is also constant

V₀ = i (R_L + R)

therefore the voltage in the battery is the highest V₀

the voltage across the wire if it is ideal is zero V_r = 0, if it is ideal its resistance is zero

therefore the voltage on the lamp is equal to the voltage of the battery

V_{battery} = V_{Lamp} > V_{wire}