Question

What maximum power can be generated from an 18-V emf using any combination of a 6.0-Ohm resistor and a 9.0-Ohm resistor?

Answer 1

Answer:

90 W

Explanation:

The power generated from a power supply in a circuit with a total resistance R is

$P=\frac{V^2}{R}$ (1)

where

V is the emf of the source

R is the total resistance of the circuit

Here we have:

V = 18 V (emf of the power source)

We have two resistors of

$R_1=6.0 \Omega\\R_2 = 9.0 \Omega$

From eq.(1), we see that the maximum power is generated when the total resistance is minimum: therefore, when the two resistors are connected in parallel.

In that case, the total resistance is given by:

$R=\frac{R_1 R_2}{R_1+R_2}=\frac{(6.0)(9.0)}{6.0+9.0}=3.6 \Omega$

So, the maximum power is:

$P=\frac{18^2}{3.6}=90 W$

Answer 2

The maximum power produced by the given emf would be as follows

$90W$

Find the power

Given that,

V $= 18 V$

$R_{1} = 6$Ω

$R_{2}$ $= 9$Ω

As we know,

$P = V^2/R$

Here,

V is denoted as the emf

R denotes total resistance

To find,

P = ?

We will find the value of R first,

$R =$ $(R_{1} R_{2})/(R_{1} + R_{2})$

$= [(6)(9)]/(6 + 9)$

$= 3.6$Ω

Therefore,

$P = (18^2)/3.6$

∵ Maximum Power = $90W$

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