# What is the equivalent resistance and capacitance?

1. A 100 ohm resistor is joined in parallel with a 47 ohm resistor. What is the equivalent resistance?

2. Three capacitors of 2.0, 5.0, and 20 microF are joing together in parallel. What is their equaivalent capacitance?

3. Three capacitors of 1.0, 1.5, and 5.0 uF are joined together in series. What is their equivalent capacitance?

4. A single household circuit operates at 120V and is protected by a 15-A circuit breaker. How many 60-W lamps can be operated at the simultaneously without tripping the circuit breaker?

5. An elevator in a 20-story building is used to raise a 7200-N load 50 m. How much will it cost to raise the load if electricity costs $0.078/kWh? Assume that the elevator system is 50% efficient - that is, that the energy expended in raising the load is half of the total energy consumed.

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#### Solution Preview

1.

R1 = 100 ohm

R2 = 47 ohm

The equivalent resistance of parallel resistances

R|| = R1*R2/(R1+R2) = 100*47/(100+47) = 31.97 ohm --Answer

2.

C1 = 2.0 microF

C2 = 5.0 microF

C3 = 20 microF

Because in parallel the equivalent capacitor is the sum all the capacitances,

C|| = C1 + C2 + C3 = 2.0+5.0+20 = 27.0 micro ...

#### Solution Summary

Solution provides calculations and answers for questions 1-5.