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Fundamentals Of Physics
Found in: Page 797

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Short Answer

In Figure ,R1=6.00 V , R2 =18.0Vand the ideal battery has emf ε=12.0 V.

(a) What is the size of current i1?

(b) What is the direction (left or right) of current i1 ?

(c) How much energy is dissipated by all four resistors in 1.00 min?

  1. The size of current i1 is 0.333  A
  2. The direction of current i1 is rightward
  3. The energy dissipated by all four resistors in 1.0  min is 720  J
See the step by step solution

Step by Step Solution

Step 1: Write the given data:

R2=18.0 ΩR1=6.00ΩV=12.0  V

Time, t=1.00min=60.0  s

Step 2: Understanding the concept

Use the concept of series as well as parallel resistances. Using that, we can find total resistance. Then, we have to use Ohm’s law V=IR to find total current.

Write the formula for series and the parallel resistance:


Write the formula for the electrical energy:


Step 3: (a) Calculate the size of current

Here all R2are connected in parallel. So, the equivalent of those is R .

1R =1R2+1R2+1R21R=118+118+118R=6.00

Now R1 and R are in series, so, equivalent of those is R'.

R'=R1+RR'=6.00+6.00 R'=12.0

Now, according to Ohm’s law, total current l is as follow:

I=VR'I=12.012.0I=1.00 A

Now,current i1 , here I is the total current through R and R' and R is the combination of three parallel resistances R2.So, the current through each R2. is one third that of the total current.


i1=I3=1.003=0.333  A

Step 5: (b) Calculate the direction (left or right) of current i1

Direction of current:

Consider the positive current direction from thepositive terminal to the negative terminal. So, the current l is clockwise means it is rightwards.

Step 5: (c) Calculate how much energy is dissipated by all four resistors in 1.00 min

Energy dissipated:

E=I2R't Substitute the values and solve for the energy dissipated as:

E=1.002×12.0×60.0E=720  J

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