One junction of a certain thermoelectric couple is at a fixed temperature r T and the other junction is at temperature T . The thermo electromotive force for this is expressed by `E=K(T-T_(r ))[T_(0)-(1)/(2)(T+T_(r ))]`. At temperature `T=(1)/(2)T_(0)`, the thermoelectric power is

Options

A. `(1)/(2)KT_(0)`
B. `KT_(0)`
C. `(1)/(2)KT_(0)^(2)`
D. `(1)/(2)K(T_(0)-T_(r))^(2)`

Explanation

To solve the problem, we need to find the thermoelectric power \( S \) at the temperature \( T = \frac{1}{2} T_0 \). The thermoelectric power is given by the derivative of the electromotive force \( E \) with respect to temperature \( T \).

### Step-by-Step Solution:

1. **Given Formula**:
The electromotive force \( E \) is given by:
\[
E = K(T - T_r)\left[T_0 - \frac{1}{2}(T + T_r)\right]
...