What is the value of resistor R in the figure(Figure 1) if V=7V and I=6A?

What is the value of resistor R in the figure(Figure 1) if V=7V and I=6A?

What is the value of resistor R in the figure(Figure 1) if V=7V and I=6A?

Express your answer using two significant figures.

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Answer:

1/10 + 1/15 + 1/R = 1/R(net)

according to Ohm’s Law: I*R(net) = V

=> R(net) + V/I => 7/6

=> 1/R(net) = 6/7 = 1/10 + 1/15 + 1/R

=> 6/7 – 1/10 – 1/15 = 1/R

=> 0.69047619047619047619047619047619 (used Windows Calculator)

=> R = 0.69047619047619047619047619047619 ^ -1

=> R = 1.4482758620

=> R = 1.44 ohms

V = 7 V

I = 6 A

Req = V / I = 7/6 Ω

Req = Equivalent resistance of the combination

of 10 Ω, 15 Ω and R Ω connected in parallel

=> 1/Req = (1/10 + 1/15 )+ 1/R

=> 1/(7/6) = 1/6 + 1/R

=> 6/7 = 1/6 + 1/R

=> 1/R = 6/7 – 1/6 = 29/42

=> R = 42/29 = 1.4 Ω

v=IR

7=6*R

R=7/6

R=1.17ohm

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