A plug-in transformer, like that in Figure 23.29, supplies 9.00 V to a video game system. (a) How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 400 turns? (b) What is its input current when its output is 1.30 A?

Video Transcript

This is College Physics Answers with Shaun Dychko. A 9.00 volt transformer is being used to power a video game system and we'll label this V s for 'secondary'— this is the output voltage of a transformer— and the input voltage is 120 volts— it's being used in North America I suppose or maybe South America but not in Europe because that's 240 volts— anyway, the input voltage is the primary voltage and the number of turns in the primary we are told is 400 turns and the question is how many turns of wire must be in the secondary? So voltage in the secondary divided by voltage in the primary equals the number of turns in the secondary divided by the number of turns in the primary. So we can solve for N s by multiplying both sides by N p and we have N s equals N pV s over V p. So that's 400 turns times 9.00 volts divided by 120 volts and there must only be 30 turns in the secondary coil in order to produce this step down in voltage— this is a step-down transformer. And part (b) asks what is the current in the primary given that the current in the secondary is known to be 1.30 amps? So the input current, in other words, is what we are asking for. And so we can solve for I p by multiplying both sides... by the way, this is a formula for current in a transformer: we have I s over I p equals N p over N s. So we'll solve for I p by multiplying both sides by I pN s over N p and we have I p equals N sI s over N p. So that's 30 turns in the secondary multiplied by 1.30 amps coming out of the secondary divided by 400 turns in the primary and so the current going in the primary is 9.75 times 10 to the minus 2 amps.