Siix lead-acid type of secondary cells, each of emf 2.0 V and internal resistancce `0.015 Omega` are joined in series to provide a supply to a resistance of `8.5Omega`. Determine : (i) the current draw from the fupply and (ii) its terminal voltage.

Answer

To solve the problem, we will follow these steps:

### Given Data:
- Number of cells, \( n = 6 \)
- EMF of each cell, \( E = 2.0 \, \text{V} \)
- Internal resistance of each cell, \( r = 0.015 \, \Omega \)
- External resistance, \( R = 8.5 \, \Omega \)

### Step 1: Calculate the Total EMF
The total EMF (\( E_{\text{total}} \)) of the series combination of cells is given by:
\[ E_{\text{total}} = n \times E \]
Substituting the values:
\[ E_{\text{total}} = 6 \times 2.0 = 12.0 \, \text{V} \]

### Step 2: Calculate the Total Internal Resistance
The total internal resistance (\( r_{\text{total}} \)) of the series combination is given by:
\[ r_{\text{total}} = n \times r \]
Substituting the values:
\[ r_{\text{total}} = 6 \times 0.015 = 0.09 \, \Omega \]

### Step 3: Calculate the Total Resistance in the Circuit
The total resistance \( R_{\text{total}} \) in the circuit is the sum of the total internal resistance and the external resistance:
\[ R_{\text{total}} = r_{\text{total}} + R \]
Substituting the values:
\[ R_{\text{total}} = 0.09 + 8.5 = 8.59 \, \Omega \]

### Step 4: Calculate the Current Drawn from the Supply
Using Ohm's law, the current \( I \) drawn from the supply can be calculated using the formula:
\[ I = \frac{E_{\text{total}}}{R_{\text{total}}} \]
Substituting the values:
\[ I = \frac{12.0}{8.59} \approx 1.40 \, \text{A} \]

### Step 5: Calculate the Terminal Voltage
The terminal voltage \( V \) can be calculated using the formula:
\[ V = E_{\text{total}} - I \times r_{\text{total}} \]
Substituting the values:
\[ V = 12.0 - (1.40 \times 0.09) \approx 12.0 - 0.126 \approx 11.874 \, \text{V} \]

### Final Answers:
(i) The current drawn from the supply is approximately \( 1.40 \, \text{A} \).

(ii) The terminal voltage is approximately \( 11.874 \, \text{V} \).

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