What is the Potential Difference Between c and d in This Circuit?

[cnh1995]

VR1V_{R1} = VinV_{in} R1R1+R2+Rj+R(n−1)+Rn\frac{R1}{R1 + R2+R_j+R_(n-1)+R_n}

Right?

Right.

I am unable to write the same for capacitors

That's because series capacitors don't add directly.

 

[cnh1995]

I'll give it a try

VC1V_{C1}=VinV_{in} C2CjCn−1Cn+C1CjCn−1Cn+C1C2Cn−1+Cn+C1C2CjCn+C1C2CjCn−1C1C2CjCn−1Cn

I believe the summation part in the numerator should be in the denominator. Also, you can verify this formula by putting n=2.

 

[ehild]

in the picture why $V_{Rn}$ =$I$$R_n$ and $V_{Cn}$=$\frac{Q}{C_n}$ is not shown

It is just typo. The last formulas were meant V_Rn=IR_n and V_Cn=Q/C_n
Keep in mind that the voltages add when the components are connected in series. The total voltage across the chain of resistors is
V_in = I (R1+R2+...+Rn),
and in case of series capacitors is
V_in=Q/(C1+C2+...+CN).

In case of resistors,
$I=\frac{V_{in}}{R_1+R_2+...R_n}$ and the voltage across the i-th element is $V_i=IR_i=V_{in}\frac{R_i}{R_1+R_2+...+R_n}$.

In case of capacitors,
$Q=\frac{V_{in}}{1/C_1+1/C_2+...+1/C_n}$ and the voltage across the i-th element is $V_i=Q/C_i=V_{in}\frac{1/C_i}{1/C_1+1/C_2+...+1/C_n}$.

 

[gracy]

i-th element

Any random element ?

 

[gracy]

Should not it be $V_i$=Q/$C_i$=$V_{in}$$\frac{1/C_i}{1/C_1+1/C_2+...+1/C_n}$

 

[gracy]

Similarly here
$V_i$=$I$$R_i$=$V_{in}$$\frac{R_i}{R_1+R_2+...+R_n}$

 

[epenguin]

Read #40. I have added to the "Relevant equations". When you take these into account you can solve this problem in 10 seconds... unless you prefer to be a pedantic student, but I see no virtue in taking days you could use for other study or something else over a 10 s problem.

 

[ehild]

Should not it be $V_i$=Q/$C_i$=$V_{in}$$\frac{1/C_i}{1/C_1+1/C_2+...+1/C_n}$

Yes, thank you . I corrected it. You see how easy it is to make mistakes!
Yes i denotes any random element.
You can also notice that in case all n components of the chain are equivalent, the voltage across one of them is V_in/N . That was epenguin suggested you in #40.

 

[gneill]

in the picture why $V_{Rn}$ =$I$$R_n$ and $V_{Cn}$=$\frac{Q}{C_n}$ is not shown

Good catch! That's down to me getting sloppy with the cut & paste to duplicate the expressions, forgetting to "touch up" those entries.

I've updated the picture.