8. Power in electric circuits

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Example: Two resistors, R1 = 5 , R2 = 10 , are connected in series. The battery has voltage of V = 12 V. a) Find the electric power delivered by the batteryb) Find the electric power dissipated in each resistor

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211 Power in the resistor R1:

WARIP RR 4.6)10()8.0( 22

222 Power in the resistor R2:

The total power: WWWPPP RRtot 6.94.62.321

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R

R

12

10

5

2

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Example: Two resistors, R1 = 5 , R2 = 10 , are connected in parallel. The battery has voltage of V = 12 V. a) Find the electric power delivered by the batteryb) Find the electric power dissipated in each resistor

Power in the resistor R1:

Power in the resistor R2:

The total power:

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12

10

5

2

1

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100

110

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Fuses and Circuit breakersTo prevent some damage in the electric circuit we use electric fuses. It will blow up due to a large heat if the current flowing through it will be larger than a certain critical value (10 A, 20 A, 100 A, etc.). Fuses are one-use items – if they blow, the fuse is destroyed and must be replaced.Circuit breakers, which are now much more common, are switches that will open if the current is too high; they can then be reset.

Example: Consider an electric hair dryer and electric iron which have 1000 W and 1500 W power when running on 120 V

Total power:

Total current (when used simultaneously):

WWWPtotal 250015001000

The fuse must to keep a current larger than 20.8 A

Example: How much energy does a typical appliance use? Let’s look at 1000 W hair dryer. We use it for 10 minutes, electricity costs ~10 cents per kWh.

How much did running the hair dryer cost?

cents 66.1min/60

min 10

hkW

cents 10 kW)(1 cost

h

Example: Three wires, of the same diameter, are connected in turn between two points maintained at a constant potential difference. Their resistivities and length are: 1) ρ and L; 2) 2ρ and 2L; 3) 0.9ρ and L. Rank the wires according to the rate at which energy is transferred to thermal energy within them.

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LR

22

L

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2

1 L

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22

2

2

L

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312 PPP

1 kWh = 1000 J/s x 3 600 s = 3 600 000 J

What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time (E = Pt). We have been measuring energy in joules, but the electric company measures it in kilowatt-hours, kWh. Electric meter monitors power consumption.

9. EMF and terminal voltage

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An real emf device: r internal =0

Disconnected battery: R=∞

0

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r

a

b

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ab

Example: An electric bulb with resistance of 22 Ω is connected to the battery with emf of 12 V and internal resistance 2 Ω. Find current, terminal voltage, and potential difference across the bulb.

V11225.0

V11)2)(A5.0(V12

R

AIRV

IrVab

A5.0222

V12

rRI

-+

A

V

I I

abV

2r

22R

V12

ba