Learn potential difference across resistor & battery, terminal potential difference. Practice equation to calculate potential difference across combination of battery and resistance.

- Consider a resistance in which current is flowing, as shown in figure.

- Current always flow in a resistor from point of higher potential to point of lower potential.

- An ideal battery B is shown in figure.

- Consider a circuit consisting of two ideal batteries \(B_1\) and \(B_2\) as shown in figure

**For B**_{1}

Direction of current : P to Q

Potential difference across B_{1} : V_{P}–V_{Q} (V_{P} is at positive terminal)

(V_{Q} is at negative terminal)

**For B**_{2}

Direction of current : T to S

Potential difference across B_{2} : V_{S}–V_{T} (V_{S} is at positive terminal)

(V_{T} is at negative terminal)

- In case of an ideal battery, potential difference across the terminal of battery is independent of direction of current.

- Consider a resistor of R \(\Omega\) through which current \(I\) is flowing.
- Potential at point P = V volt
- Potential at point Q = V
_{P}– (voltage drop across resistor 'R') -
V

_{Q}= V_{P}– IRV

_{Q}=V – IR

V_{Q} =V_{P} + IR

V_{Q} = V + IR

- Consider a battery with e.m.f \(\mathcal{E}\).
- For an ideal battery, potential difference across terminal is independent of direction of flow of current.

Potential at point P = V volt

Potential at point Q,

V_{Q} = V_{P }– e.m.f of the battery

\(V_{Q}=V-\mathcal E\)

V_{Q} = V_{P }– e.m.f. of battery

\(V_{Q}=V-\mathcal E\)

[Potential at point is independent of direction of current]

V_{Q} = V_{P}+ e.m.f of battery

\(V_{Q}=V+\mathcal E\)

V_{Q} = e.m.f of battery + V_{P}

\(V_Q=\mathcal E+V\)

[Potential at point across battery is independent of direction of current]

- Consider a circuit in which a battery with e.m.f is connected with load resistance R, through which current is flowing in the circuit.
- Potential at point P is V
_{P}.

- To calculate potential at point Q, mark a point T between battery and resistance.

- Divide the circuit into two parts at T and then calculate separately.

So,

\(V_Q=V_P+\mathcal{E}–IR\)

- Consider a circuit in which a battery with e.m.f is connected with load resistance R, through which current is flowing in the circuit.
- Potential at point P is V
_{P}.

- To calculate potential at point Q, mark a point T between battery and resistance.

- Divide the circuit into two parts at T and then calculate separately.

So, \(V_Q=V_P-\mathcal{E}–IR\)

- Generally, the resistance of connecting wires is assumed to be zero.
- A practical battery is made of some material which offers resistance to flow of charge within the battery. This resistance is known as internal resistance.

**For ideal battery**

- Internal resistance, r = 0
- Potential difference = \(\mathcal{E}\) (e.m.f of battery)

**For practical battery**

- Internal resistance r\(\neq\)0
- To calculate potential difference of a practical battery, consider a circuit,as shown in figure.

- Current I is flowing in a circuit having battery (practical) with e.m.f \(\mathcal{E}\) and internal resistance r.
- Potential difference across terminal (P and Q)

\(\Delta V=V_P–V_Q\)

\(\Delta V=(V_P–V_C)–(V_Q–V_C)\)

\(\Delta V=\mathcal{E}\,–Ir\)

- Consider a circuit in which a battery with e.m.f is connected with load resistance R, through which current is flowing in the circuit.
- Potential at point P is V
_{P}.

- To calculate potential at point Q, mark a point T between battery and resistance.

- Divide the circuit into two parts at T and then calculate separately.

So, \(V_Q=V_P+\mathcal{E}–IR\)

- Potential at point P is V
_{P}.

- To calculate potential at point Q, mark a point T between battery and resistance.

- Divide the circuit into two parts at T and then calculate separately.

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 \(V_C=V_B–\mathcal{E}_2-I(r_2+R_2)\)