Download Problem B - Geneva Area City Schools

NAME ______________________________________ DATE _______________ CLASS ____________________
Electromagnetic Induction
Problem B
rms CURRENTS AND emf
PROBLEM
A generator with a rms potential difference of 124 V is connected to a
85 resistor. Calculate the maximum output emf. Find the rms current
and the maximum ac current in the circuit.
SOLUTION
Given:
∆Vrms = 124 V
Unknown:
∆V
max = ?
R = 85 Ω
Irms = ?
Imax = ?
Choose the equation(s) or situation: Use the equation for the rms potential difference to find the rms potential difference.
∆Vrms = 0.707 ∆Vmax
Use the equation for rms current to find Imax.
Irms = 0.707 Imax
Rearrange the equation(s) to isolate the unknown(s): Rearrange the definition
for resistance to calculate the rms current.
∆Vrms
Irms = 
R
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Rearrange the equation relating rms current to maximum current so that maximum current is calculated.
I s
Imax = rm
0.707
Rearrange the equation relating rms potential difference to maximum potential
difference so that maximum potential difference is calculated.
∆Vrms
∆Vmax = 
0.707
Substitute the values into the equation(s) and solve:
∆Vrms 124 V
∆Vmax = 
=  = 175 V
0.707 0.707
∆Vrms 124 V
Irms = 
=  = 2.1 A
R
85 Ω
I s 2.1 A
=  = 3.0 A
Imax = rm
0.707 0.707
Evaluate: The maximum values for potential difference and current are a little
less than three-halves (1.5 times) the rms values, as expected.
Problem B
Ch. 20–3
NAME ______________________________________ DATE _______________ CLASS ____________________
ADDITIONAL PRACTICE
1. Suppose you build a hydroelectric turbine in your back yard along a
river. The turbine is connected to a generator which can provide a rms
potential difference of 320 V onto a 100 Ω load. Calculate the maximum
output emf. Find the rms current and the maximum ac current in the
circuit.
2. Some wind turbines in the United States can provide an rms current of
1.3 A. Calculate the maximum ac current.
3. In Iceland, people harness geothermal energy by placing pipes deep into
the Earth in order to tap hot-water aquifers. Steam from these aquifers
spins a turbine that is connected to a generator. Suppose such a generator
can provide a rms current of 2.5 A and an rms potential difference of
22 kV. Calculate the maximum ac current. Find the resistance of the
load.
4. In Denmark, farmers and people living in rural areas harness wind energy to spin a turbine that is coupled to a generator. The generator can
provide an rms current of 1.7 A and an rms potential difference of 220 V.
Calculate the maximum ac current and the maximum output emf.
5. A generator can provide a maximum ac current of 1.2 A and a maximum
output emf of 211 V. Calculate the rms current, the rms potential difference, and the resistance in the circuit.
6. A generator can provide a maximum output emf of 170 V. Calculate the
rms potential difference.
8. Off the western coast of Scotland, turbines are placed in deep ocean
water so that ocean waves can spin them. The turbines are connected to a
generator, which produces electricity for the locals. These turbines can
supply an rms current of 2.1 A on a 16 kΩ load. Calculate the maximum
ac current. How much power is supplied?
9. A wind turbine is built to service farmers in England. The turbine is connected to a generator, which can supply a rms current of 1.3 A on a
12 kΩ load. If the rms potential difference is 15.6 kV, find the maximum
output emf provided by the wind turbine. Calculate the maximum ac
current. How much power is supplied?
10. The total world potential for hydroelectric generation is 1.2 million MW,
however, not all of it has been harnessed. Suppose the world’s rms current is 2.2 × 1010 A and it supplies a load of 6.1 × 10–10 Ω. Calculate the
total maximum ac current that is harnessed. How much total power can
be supplied with this current?
Ch. 20–4
Holt Physics Problem Bank
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. Suppose you measure a circuit with a voltmeter. You measure a rms potential difference of 115 V and a resistance of 50.0 Ω. Find the maximum
ac current and the rms current in the circuit.