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A transformer has 500primary turns and 1012 secondary turns. (a) If role="math" localid="1663224210090" Vpis 120 V(RMS),whatVs is with an open circuit? (b) If the secondary now has a resistive load ofrole="math" localid="1663224020026" 15Ω, what is the current in the primary? (c) If the secondary now has a resistive load of 15Ωwhat is the current in the secondary?

Short Answer

Expert verified
  1. The secondary voltage at Vp=120V, with an open circuit is 2.4V.

b. Current through primary ,when secondary has resistive load 15Ωis 3.2×10-3A.

c. Current through secondary when secondary has resistive load 15Ωis 0.16A.

Step by step solution

01

Listing the given quantities:

Primary turns areNp=500.

Secondary turns are Ns=10.

02

Understanding the concept of Ohm’s law and transformer:

A transformer is a device that transfers electrical energy from one alternating current circuit to one or more other circuits by either increasing (stepping up) or decreasing (stepping down) the voltage.

Ohm's law states that the current flowing through a conductor between two points is directly proportional to the voltage across both points.

Use the equation related to primary and secondary coil voltages and currents with the number of turns.

03

(a) Calculation of the Secondary voltage at with an open circuit:

Atsecondary voltage with an open circuit:

Vp=120V

Using the equation as given below.

VsVp=NsNp

Rearranging it for Vs, you have

Vs=VpNsNp=12010500=2.4V

Hence, the secondary voltage at Vp=120Vwith an open circuit is 2.4 V .

04

(b) Calculation of the Current through primary when secondary has resistive load 15Ω

Current through primary when secondary has resistive load15Ω.

Here,lsis unknown, so we can find from Ohm’s law:

localid="1663226024205" IpIs=NsNp

Using the equation for current in transformer,

IpIs=NsNp

Rearranging it for primary current, we get

Ip=IsNsNp=0.1610500=3.2×10-3A

Hence, the current through primary when secondary has resistive load 15Ωis 3.2×10-3A.

05

(c) Calculation of the current through secondary when secondary has resistive load 15Ω:

Current through secondary when secondary has resistive load15Ω.

As current in secondary in the above part,

Is=0.16A

Hence, the current through secondary when secondary has resistive load 15Ωis 0.16 A.

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