Learn potential difference across resistor & battery, terminal potential difference. Practice equation to calculate potential difference across combination of battery and resistance.
Direction of current : P to Q
Potential difference across B1 : VP–VQ (VP is at positive terminal)
(VQ is at negative terminal)
Direction of current : T to S
Potential difference across B2 : VS–VT (VS is at positive terminal)
(VT is at negative terminal)
VQ = VP – IR
VQ =V – IR
VQ =VP + IR
VQ = V + IR
For ideal battery
For practical battery
\(\Delta V=V_P–V_Q\)
\(\Delta V=(V_P–V_C)–(V_Q–V_C)\)
\(\Delta V=\mathcal{E}\,–Ir\)
So, \(V_Q=V_P+\mathcal{E}–IR\)
So, \(V_Q=V_P–\mathcal{E}–IR\)
A \(V_C=V–[(\mathcal{E}_1+\mathcal{E}_2)+I(r_1+R_1+r_2+R_2)]\)
B \(V_C=V–[(\mathcal{E}_1-\mathcal{E}_2)+I(r_1+R_1-r_2+R_2)]\)
C \(V_B=V_A–\mathcal{E}_1-I(r_1+R_1)\)
D \(V_C=V_B–\mathcal{E}_2-I(r_2+R_2)\)
Potential at point P = V volt
Potential at point Q,
VQ = VP – e.m.f of the battery
\(V_{Q}=V-\mathcal E\)
VQ = VP – e.m.f. of battery
\(V_{Q}=V-\mathcal E\)
[Potential at point is independent of direction of current]
VQ = VP+ e.m.f of battery
\(V_{Q}=V+\mathcal E\)
VQ = e.m.f of battery + VP
\(V_Q=\mathcal E+V\)
[Potential at point across battery is independent of direction of current]
So,
\(V_Q=V_P+\mathcal{E}–IR\)
So, \(V_Q=V_P-\mathcal{E}–IR\)