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1 Mutual / Self-Induction – Learning Outcomes HL: Define and discuss mutual induction for two adjacent coils. HL: Demonstrate mutual induction. HL: Define and describe self-induction. HL: Demonstrate self-induction. Give the structure and principle of operation of a transformer. Demonstrate a transformer. Solve problems about transformers. Give some uses of transformers. 2 Mutual / Self-Induction – Learning Outcomes Describe the effect of inductors on a.c. Describe the effect of capacitors on a.c. Give the uses of inductors. 3 HL: Mutual Induction Mutual induction occurs when two coils are adjacent to each other. If the magnetic field in one coil changes, an emf is induced in the other. This happens with a.c. The size of the induced emf depends on: the distance between the coils (closer yields more emf), whether the coils have the same core (yields more emf), the number of turns in each coil (more yields more emf). aka Faraday’s experiment 4 HL: Demonstrate Mutual Induction 1. Set up two circuits – one consists of a galvanometer and a coil of wire (circuit 1), while the other consists of a d.c. power supply, open switch, and coil of wire (circuit 2). 2. Move the coils next to each other. 3. Close the switch in circuit 2 and note an instantaneous deflection in the galvanometer needle in circuit 1. 4. Leave the switch closed, noting no deflection in the galvanometer needle in circuit 1. 5. Open the switch in circuit 2 and note an instantaneous deflection in the galvanometer needle in circuit 1. 6. Deflection only occurs when the magnetic field due to circuit 1 changes. There is no deflection with constant current. 5 HL: Demonstrate Mutual Induction To get “Faraday’s apparatus”, include an iron ring with a coil wrapping around either side. 6 HL: Self Induction Whenever the current passing through a coil changes, its magnetic field changes. This change induces an emf in the same coil which opposes the change. This is called a back emf and the phenomenon is called self induction. Coils which exhibit noticeable levels of self induction are called inductors. 7 HL: Demonstrate Self Induction 1. Connect a coil with a soft iron core in series with a bulb, power supply, and switch. 2. Close the switch. 3. Note that the bulb does not reach full brightness immediately: it gradually gets brighter. 4. Thus, the coil exhibited self-induction: as the current increased, it created a changing magnetic field, inducting a back emf in the coil. 8 Transformers We discussed transformers previously in domestic circuits. Recall that electricity is sent around the country at high voltage to avoid heat losses by Joule’s Law (𝑃 ∝ 𝐼 2 ), then transformed down to ~230 V for local use. Transformers consist of two coils wrapped around the same iron core with different numbers of turns. by Fizped – CC-BY-SA-3.0 9 Transformers The primary coil with 𝑁𝑃 turns is connected to a.c. of voltage 𝑉𝑖 , which results in a changing magnetic field. This flux induces an emf 𝑉𝑜 in the secondary coil which has 𝑁𝑆 turns. The ratio of the voltages between the coils is the same as the ratio of the number of turns. 𝑉𝑖 𝑉𝑜 = 𝑁𝑃 𝑁𝑆 by Fizped, edited under CC-BY-SA-3.0 10 To Demonstrate a Transformer 1. Set up circuit 1 with a coil in series with an a.c. supply, measuring the voltage of the coil with a voltmeter. 2. Set up circuit 2 with a voltmeter measuring the voltage of a second coil. 3. Wrap both coils around the same iron core. 4. Note that the ratio of the voltages is the same as the ratio of the number of turns in the coils. symbol for a transformer 11 Uses of Transformers Mains electricity is generated at low voltage, then a “step-up transformer” increases the voltage for national transmission. A “step-down transformer” is then used to reduce the voltage to ~230 V for local use. Many appliances (e.g. tvs, computers, microwaves) will not work well at 230 V, so will have an internal transformer to get the appropriate voltage. 12 Inductors and a.c. Inductors act as regular resistors when in a d.c. circuit. In an a.c. circuit, the changing current causes a changing magnetic field, causing self-induction (and thus, a back emf) in the inductor. Inductors are used to: smooth out variations in d.c. tune radios, dim lights as part of dimmer switches. 13 Capacitors and a.c. Recall that capacitors will not conduct d.c. once they are charged. In a.c., the changing direction of the current means that capacitors are in a constant cycle of charging and discharging, which effectively means they conduct a.c. Higher capacitance capacitors will offer less resistance to a.c.