How Do Differential Equations Model Electric Circuits in Medical Devices?

AI Thread Summary
Differential equations are essential for modeling electric circuits in medical devices like pacemakers, where components such as batteries, capacitors, and resistances interact. The problem involves determining the electric tension E applied to the heart over time, with the capacitor charging and discharging based on the switch's position. The discussion raises questions about the nature of the equation, specifically whether it is first-order linear and homogeneous, and seeks guidance on finding the initial voltage. Understanding these concepts is crucial for solving the problem effectively. Clarification on the problem may be needed for better assistance.
itzela
Messages
34
Reaction score
0
Hi Guys... I'm trying to learn diff.eq on my own and I'm stuck on a problem and I don't even know where or how to begin:

the problem is: the pacemaker shown in the figure (first attatchment) is made up of an electric battery, a small capacitor, and the heart which functions like a resistence in the circuit. When the commuter S connects to P the capacitor charges, when S is connected to Q the capacitor discharges sending an electric shock to the heart. During this time the electric tension E applied to the heart is given by: (second attatchment).

The resistance and the capacitance are both constant...
what is:
E(t)= ? E(t1) = Eo

Would it be a first order linear equation?
Is it homogenous?
What would be the value of the initial voltage?

- i translated it directly from spanish so if further clarifying of the problem is needed please let me know.
 

Attachments

  • prob-cont.JPG
    prob-cont.JPG
    5.8 KB · Views: 442
  • prob-cont2.JPG
    prob-cont2.JPG
    1.1 KB · Views: 442
Physics news on Phys.org
any advice on how to start?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »
Thread 'Minimum mass of a block'

Thread 'Minimum mass of a block'

Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
View full post »

Similar threads

Calculation of current in driven series RLC circuit
Replies
8
Views
2K
I Thought I Understood Gauss' Law (Sheets)
Replies
26
Views
2K
Capacitor Questions Charging and Discharging
Replies
4
Views
3K
Final potential difference of a 2 capacitor system
Replies
3
Views
3K
How Much Charge Does a Defibrillator Capacitor Store After 1.10 Seconds?
Replies
2
Views
2K
Electric field in a capacitor with a dielectric
Replies
5
Views
2K
Electric Potential Difference in a Circuit with Emf Devices
Replies
4
Views
2K
Finding the voltage of a circuit
Replies
2
Views
4K
RC circuit - Rate o'energy dissipated = rate o'energy stored
Replies
8
Views
3K
Entropy change in an RC circuit
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top