Question: In Figure, the current in resistance 6 isi6 =1.40 Aand the resistances are R1=R2=R3=2.00Ω,R4=16.0Ω,R5=8.00ΩandR6=4.00Ω.What is the emf of the ideal battery?

Short Answer

Expert verified

Answer

The emf of the ideal battery is 48.3 V .

Step by step solution

01

Given

  1. Current I6=I5=1.40A
  2. Resistances R1=R2=R3=2.00Ω,R4=16.0Ω,R5=8.00Ω,R6=4.00Ω
02

 Step 2: Determine the concept

Use the Ohm’s law and Kirchhoff’s loop rule and the junction rule to find the emf of the ideal battery.

Write the formula for the voltage and the current:

V=IR∑V=0∑Ii=∑Io

03

Calculate the current through  

The total voltage across R4 is equal to the sum of the voltages across R5 and R6 .

Therefore,

V4=I5R5+I6R6

V4=1.40A8.00Ω+1.40A4.00ΩV4=16.8V

The current through R4 is then calculated as:

role="math" localid="1662964664780" I4=V4R4I4=16.8V16.0ΩI4=1.05A

04

Calculate the potential across R2 

According to the junction rule, the current in R2 is

I2=I4+I5I2=1.05A+1.4AI2=2.45A

So, its voltage is

V2=I2R2V2=2.45A2.00ΩV2=4.90V

05

Calculate the current through  R3 

By the loop rule, the voltage across R3 is

V3=V2+V4V3=4.90V+16.8VV3=21.7V

So, the current through R3 is

I3=V3R3I3=21.7V2.0ΩI3=10.85A

06

Calculate the voltage across  R1

Now, by applying the junction rule, we can get the current through R1

I1=I2+I3

Substitute the values and solve as:

I1=2.45A+10.85AI1=13.3A

Therefore, the voltage across R1 is as follows:

V1=I1R1

Solve further as:

V1=13.3A2.00ΩV1=26.6V

07

Calculate the emf of the battery

Now, by the loop rule,

ε=V1+V3

Substitute the values and solve as:

ε=26.6V+21.7Vε=48.3V

Therefore, the emf of the ideal battery is 48.3 V

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Fig. 27-54, the resistances areR1=1.0 ΩandR2=2.0 Ω , and the ideal batteries have emf ε1=2.0Vand ε2=ε3=4.0V. What are the (a) size and (b) direction (up or down) of the current in battery 1, the (c) size and (d) direction of the current in battery 2, and the (e) size and (f) direction of the current in battery 3? (g) What is the potential difference Va−Vb?

Question: (a) In Fig. 27-4a, show that the rate at which energy is dissipated in Ras thermal energy is a maximum when R =r. (b) Show that this maximum power is P=ε2/4r.

Suppose that, while you are sitting in a chair, charge separation between your clothing and the chair puts you at a potential of 200 V, with the capacitance between you and the chair at 150 pF. When you stand up, the increased separation between your body and the chair decreases the capacitance to 10 pF. (a) What then is the potential of your body? That potential is reduced over time, as the charge on you drains through your body and shoes (you are a capacitor discharging through a resistance). Assume that the resistance along that route is 300GΩ. If you touch an electrical component while your potential is greater than 100V, you could ruin the component. (b) How long must you wait until your potential reaches the safe level of 100V?

If you wear a conducting wrist strap that is connected to ground, your potential does not increase as much when you stand up; you also discharge more rapidly because the resistance through the grounding connection is much less than through your body and shoes. (c) Suppose that when you stand up, your potential is 1400 Vand the chair-to-you capacitance is 10pF. What resistance in that wrist-strap grounding connection will allow you to discharge to100V in 0.30 s, which is less time than you would need to reach for, say, your computer?

In Fig. 27-5a, find the potential difference acrossR2ifε=12V,R1=3.0Ω,R2=4.0ΩandR3=5.0Ω


Res-monster maze.In Fig. 27-21, all the resistors have a resistance of4.0Ω and all the (ideal) batteries have an emf of 4.0 V. What is the current through resistor R? (If you can find the proper loop through this maze, you can answer the question with a few seconds of mental calculation.)

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free