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A resistor with resistance Ris connected to a battery that has emf 12.0 V and internal resistance r=0.40Ω. For what two values of R will the power dissipated in the resistor be 80.0 W ?

Short Answer

Expert verified

The two values of Rare 0.2Ωand 0.8Ω.

Step by step solution

01

Define the ohm’s law, resistance (R) and power (P).

Consider the formula for the Ohm’s law.

V=IR

Here, Iis current in ampere A,R is resistance in ohms role="math" localid="1655724796140" Ωand Vis the potential difference volt V.

Consider the power role="math" localid="1655724850722" (P)is the product of potential difference(V) and the current(I) and is given as follows:

P=I2R

Consider the current if the emf is ε, the internal resistance is r and the load resistance is Ris as follow:

I=εR+r

02

Determine the two resistances.

Consider the given, emf, internal resistance and the power consumed.

ε=12.0Vr=40ΩP=80.0W

Derive the equation to determine the resistance.

P=I2RP=εR+r2RP=ε2RR2+2Rr+r2R2=2Rr-ε2RP+r2=0

Substitute the values of P,randεin the equation.

R2+2R0.4-122R80+0.42=0R2-R+0.16=0R2-0.2R-0.8R+0.16=0R-0.2R-0.8=0

Solve further as,

R=0.2ΩR=0.8Ω

Hence, the two values of Rare 0.2Ωand 0.8Ωwill dissipated the power of 80.0 W .

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Most popular questions from this chapter

A light bulb glows because it has resistance. The brightness of a light bulb increases with the electrical power dissipated in the bulb. (a) In the circuit shown in Fig. Q25.14a, the two bulbs A and B are identical. Compared to bulb A, does bulb B glow more brightly, just as brightly, or less brightly? Explain your reasoning. (b) Bulb B is removed from the circuit and the circuit is completed as shown in Fig. Q25.14b. Compared to the brightness of bulb A in Fig. Q25.14a, does bulb A now glow more brightly, just as brightly, or less brightly? Explain your reasoning

Copper has 8.5×1022free electrons per cubic meter. A 71.0-cm

length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 A of

current. (a) How much time does it take for an electron to travel the length

of the wire? (b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm)

of the same length that carries the same current. (c) Generally speaking,

how does changing the diameter of a wire that carries a given amount of

current affect the drift velocity of the electrons in the wire?

Can potential difference between the terminals of a battery ever be opposite in direction to the emf? If it can, give an example. If it cannot, explain why not.

Ordinary household electric lines in North America usually operate at 120 V . Why is this a desirable voltage, rather than a value considerably larger or smaller? On the other hand, automobiles usually have 12 V electrical systems. Why is this a desirable voltage?

Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ωand 800Ω. If the two light bulbs are connected in series across a 120Vline, find (a) the current through each bulb; (b) the power dissipated in each bulb; (c) the total power dissipated in both bulbs. The two light bulbs are now connected in parallel across the120Vline. Find (d) the current through each bulb; (e) the power dissipated in each bulb; (f) the total power dissipated in both bulbs. (g) In each situation, which of the two bulbs glows the brightest? (h) In which situation is there a greater total light output from both bulbs combined?

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