Daily updates 12 August 2021

New Delhi:

India logged 37,154 fresh Covid cases and 724 deaths, taking the overall case count to 3,08,74,375 total infections registered since the start of the pandemic. More than 3 crore people have recovered so far, official data shows.

Here is your ten-point cheat sheet on this big story:

1. India's daily positivity rate - an indicator of the number of people testing positive for every 100 Covid tests - stood at 2.59 per cent this morning. It has been less than 3 per cent for 21 consecutive days.
2. India presently has 4,50,899 active Covid cases, which is 1.46 per cent of the total cases, the Health Ministry data shows. The country has witnessed a drop in cases after a very tough battle against the second wave.
3. Delhi, Haryana and Tamil Nadu eased restrictions over the weekend, while telling people to not let their guards down amid concerns over a third wave. The national capital on Sunday reported 56 fresh Covid cases, the lowest daily rise since April last year.
4. In Haryana, curbs were extended by a week while the state gave a go-ahead to cinema halls, spas and coaching institutes to open with safety protocols in place. In Tamil Nadu, restaurants, tea shops, bakeries, roadside eateries and sweet shots can stay open till 9 pm at 50 per cent capacity.
5. No cases of Delta plus variant were found in Tripura, the central government said on Sunday, a day after the state government said 90 per cent of fresh samples sent for genome sequencing tested positive for highly infectious Delta Plus variant.
6. With the government trying to chase the goal of vaccinating 108 crore adults by the end of this year, many vaccine centres have been shut in several parts of the country. Delhi vaccinated only. Mumbai and Kolkata are also witnessing a shortage.
7. India has so far given 37.73 crore vaccine doses since the vaccine drive began on January 16.
8. Australia on Monday reported its biggest daily rise in COVID-19 cases this year, fuelled by a fast-growing outbreak of the Delta variant in Sydney, news agency Reuters reported.
9. Dr Anthony Fauci, the US top coronavirus adviser, on Sunday characterised the Delta strain of COVID-19 as a "nasty variant". "It is very clear that this is a nasty variant. It has a much greater capacity of transmitting from person to person," Dr Fauci was quoted as saying by news agency ANI, adding that the COVID vaccines that are being used in America to fight the coronavirus "are working very well" and do protect against the variant.
10. Worldwide, over 18.67 crore cases have been logged since the start of pandemic; 40.30 lakh people have died.

Nodal analysis and Mesh analysis

 What is meant by nodal analysis?

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

What is the purpose of nodal analysis?

The aim of nodal analysis is to determine the voltage at each node relative to the reference node (or ground).

Steps for Nodal Analysis

1. Identify all nodes.
2. Choose a reference node. Identify it with reference (ground) symbol. ...
3. Assign voltage variables to the other nodes (these are node voltages.)
4. Write a KCL equation for each node (sum the currents leaving the node and set equal to zero)
5. Solve the system of equations from step 4.

Example 1

Find the voltage at each node

Solution

1. Identify all nodes
2. Choose a reference node. Identify it with reference (ground) symbol
3. Assign voltage variables to the other nodes (these are node voltages.)
4. Write a KCL equation for each node (sum the currents leaving the node and set equal to zero)
5. Solve the system of equations from step 4.

Example 2                              

Find the voltage at each node

 

Solution

1. Identify all nodes
2. Choose a reference node. Identify it with reference (ground) symbol
3. Assign voltage variables to the other nodes (these are node voltages.)

4. Write a KCL equation for each node (sum the currents leaving the node and set equal to zero)
5. Solve the system of equations from step 4.

Example 3

Find all the voltages

As Va = 10v and Vc = 20v , Vb can be easily found by

Mesh Current Analysis

Mesh Current Analysis is a technique used to find the currents circulating around a loop or mesh with in any closed path of a circuit.

Procedure of Mesh Analysis

• Step 1 − Identify the meshes and label the mesh currents in either clockwise or anti-clockwise direction.
• Step 2 − Observe the amount of current that flows through each element in terms of mesh currents.
• Step 3 − Write mesh equations to all meshes. Mesh equation is obtained by applying KVL first and then Ohm’s law.
• Step 4 − Solve the mesh equations obtained in Step 3 in order to get the mesh currents.

Example

Find the currents flowing in the resistor using Mesh Analysis

 

Solution

 

 

What is the difference between mesh analysis and nodal analysis?

• This method differs from the nodal method by using mesh currents instead of nodal voltages as circuit variables.
• Nodal method uses Kirchhoff's currents Law to consider nodal voltages, and Mesh method uses Kirchhoff's voltages Law to consider mesh currents. 
• Mesh is a loop, which does not contain any other loops